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{{task}}
[[wp:Floyd's triangle|Floyd's triangle]] lists the natural numbers in a right triangle aligned to the left where
- the first row is '''1''' (unity)
- successive rows start towards the left with the next number followed by successive naturals listing one more number than the line above.
The first few lines of a Floyd triangle looks like this:
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;Task: :# Write a program to generate and display here the first n lines of a Floyd triangle. (Use n=5 and n=14 rows). :# Ensure that when displayed in a mono-space font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.
360 Assembly
A very concise coding, an illustration of CISC power of the S/360 operation codes. Also an example of the use of EDMK and EX instructions. For macro usage see [[360_Assembly_macros#360_Assembly_Structured_Macros|Structured Macros]] .
* Floyd's triangle 21/06/2018
FLOYDTRI PROLOG
L R5,NN nn
BCTR R5,0 -1
M R4,NN nn*(nn-1)
SRA R5,1 /2
A R5,NN m=(nn*(nn-1))/2+nn; max_value
CVD R5,XDEC binary to packed decimal (PL8)
EDMK ZN,XDEC+4 packed dec (PL4) to char (CL8)
S R1,=A(ZN) r1=number of spaces
L R9,=A(L'ZN+1) length(zn08)+1
SR R9,R1 s=length(m)+1
SR R8,R8 k=0
LA R6,1 i=1
DO WHILE=(C,R6,LE,NN) do i=1 to nn
LA R10,PG pgi=0
LA R7,1 j=1
DO WHILE=(CR,R7,LE,R6) do j=1 to i
LA R8,1(R8) k=k+1
XDECO R8,XDEC k
LA R11,XDEC+12 +12
SR R11,R9 -s
LR R2,R9 s
BCTR R2,0 -1
EX R2,MVCX mvc @PG+pgi,@XDEC+12-s,LEN=s
AR R10,R9 pgi+=s
LA R7,1(R7) j++
ENDDO , enddo j
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
EPILOG
MVCX MVC 0(0,R10),0(R11) mvc PG,XDEC
NN DC F'14' number of rows
PG DC CL80' ' buffer
XDEC DS CL12 temp
ZN DC X'4020202020202020' mask CL8 7num
YREGS
END FLOYDTRI
{{out}}
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{{out}}
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7 8 9 10
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16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Ada
with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Command_Line;
procedure Floyd_Triangle is
rows : constant Natural := Natural'Value(Ada.Command_Line.Argument(1));
begin
for r in 1..rows loop
for i in 1..r loop
Ada.Integer_Text_IO.put (r*(r-1)/2+i, Width=> Natural'Image(rows*(rows-1)/2+i)'Length);
end loop;
Ada.Text_IO.New_Line;
end loop;
end Floyd_Triangle;
{{out}}
> ./floyd_triangle_triangle 5
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7 8 9 10
11 12 13 14 15
> ./floyd_triangle 14
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2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
ALGOL 68
{{works with|ALGOL 68G|Any - tested with release 2.8.win32}}
# procedure to print a Floyd's Triangle with n lines #
PROC floyds triangle = ( INT n )VOID:
BEGIN
# calculate the number of the highest number that will be printed #
# ( the sum of the integers 1, 2, ... n ) #
INT max number = ( n * ( n + 1 ) ) OVER 2;
# determine the widths required to print the numbers of the final row #
[ n ]INT widths;
INT number := max number + 1;
FOR col FROM n BY -1 TO 1 DO
widths[ col ] := - ( UPB whole( number -:= 1, 0 ) + 1 )
OD;
# print the triangle #
INT element := 0;
FOR row TO n DO
FOR col TO row DO
print( ( whole( element +:= 1, widths[ col ] ) ) )
OD;
print( ( newline ) )
OD
END; # floyds triangle #
main: (
floyds triangle( 5 );
print( ( newline ) );
floyds triangle( 14 )
)
{{out}}
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1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
ALGOL W
{{trans| ALgOL_68}}
begin
% prints a Floyd's Triangle with n lines %
procedure floydsTriangle ( integer value n ) ;
begin
% the triangle should be left aligned with the individual numbers %
% right-aligned with only one space before the number in the final %
% row %
% calculate the highest number that will be printed %
% ( the sum of the integeregers 1, 2, ... n ) %
integer array widths( 1 :: n );
integer maxNumber, number;
maxNumber := ( n * ( n + 1 ) ) div 2;
% determine the widths required to print the numbers of the final row %
number := maxNumber;
for col := n step -1 until 1 do begin
integer v, w;
w := 0;
v := number;
number := number - 1;
while v > 0 do begin
w := w + 1;
v := v div 10
end while_v_gt_0 ;
widths( col ) := w
end for_col;
% print the triangle %
number := 0;
for row := 1 until n do begin
for col := 1 until row do begin
number := number + 1;
writeon( i_w := widths( col ), s_w := 0, " ", number )
end for_col ;
write()
end for_row
end; % floyds triangle %
floydsTriangle( 5 );
write();
floydsTriangle( 14 )
end.
{{out}}
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1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
AppleScript
{{Trans|JavaScript}} {{Trans|Haskell}} (mapAccumL versions)
-- FLOYDs TRIANGLE -----------------------------------------------------------
-- floyd :: Int -> [[Int]]
on floyd(n)
script floydRow
on |λ|(start, row)
{start + row + 1, enumFromTo(start, start + row)}
end |λ|
end script
snd(mapAccumL(floydRow, 1, enumFromTo(0, n - 1)))
end floyd
-- showFloyd :: [[Int]] -> String
on showFloyd(xss)
set ws to map(compose({my succ, my |length|, my show}), |last|(xss))
script aligned
on |λ|(xs)
script pad
on |λ|(w, x)
justifyRight(w, space, show(x))
end |λ|
end script
concat(zipWith(pad, ws, xs))
end |λ|
end script
unlines(map(aligned, xss))
end showFloyd
-- TEST ----------------------------------------------------------------------
on run
script test
on |λ|(n)
showFloyd(floyd(n)) & linefeed
end |λ|
end script
unlines(map(test, {5, 14}))
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- compose :: [(a -> a)] -> (a -> a)
on compose(fs)
script
on |λ|(x)
script
on |λ|(f, a)
mReturn(f)'s |λ|(a)
end |λ|
end script
foldr(result, x, fs)
end |λ|
end script
end compose
-- concat :: [[a]] -> [a] | [String] -> String
on concat(xs)
if length of xs > 0 and class of (item 1 of xs) is string then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to length of xs
set acc to acc & item i of xs
end repeat
acc
end concat
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- foldr :: (b -> a -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr
-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- justifyRight :: Int -> Char -> Text -> Text
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight
-- last :: [a] -> a
on |last|(xs)
if length of xs > 0 then
item -1 of xs
else
missing value
end if
end |last|
-- length :: [a] -> Int
on |length|(xs)
length of xs
end |length|
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- 'The mapAccumL function behaves like a combination of map and foldl;
-- it applies a function to each element of a list, passing an
-- accumulating parameter from left to right, and returning a final
-- value of this accumulator together with the new list.' (see Hoogle)
-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
on mapAccumL(f, acc, xs)
script
on |λ|(a, x)
tell mReturn(f) to set pair to |λ|(item 1 of a, x)
[item 1 of pair, (item 2 of a) & {item 2 of pair}]
end |λ|
end script
foldl(result, [acc, []], xs)
end mapAccumL
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- snd :: (a, b) -> b
on snd(xs)
if class of xs is list and length of xs > 1 then
item 2 of xs
else
missing value
end if
end snd
-- show :: a -> String
on show(e)
set c to class of e
if c = list then
script serialized
on |λ|(v)
show(v)
end |λ|
end script
"{" & intercalate(", ", map(serialized, e)) & "}"
else if c = record then
script showField
on |λ|(kv)
set {k, v} to kv
k & ":" & show(v)
end |λ|
end script
"{" & intercalate(", ", ¬
map(showField, zip(allKeys(e), allValues(e)))) & "}"
else if c = date then
("date \"" & e as text) & "\""
else if c = text then
"\"" & e & "\""
else
try
e as text
on error
("«" & c as text) & "»"
end try
end if
end show
-- succ :: Int -> Int
on succ(x)
x + 1
end succ
-- unlines :: [String] -> String
on unlines(xs)
intercalate(linefeed, xs)
end unlines
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith
{{Out}}
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37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Or, defining only the relationship between successive terms:
-- floyd :: [Int] -> [Int]
on floyd(xs)
set n to succ(length of xs)
if n < 2 then
{1}
else
enumFromTo(succ(n * (pred(n)) div 2), n * (succ(n)) div 2)
end if
end floyd
-- floydN :: Int -> [[Int]]
on floydN(n)
take(n, iterate(floyd, {1}))
end floydN
-- showFloyd :: [[Int]] -> String
on showFloyd(xs)
script
on |λ|(ns)
script
on |λ|(n)
justifyRight(4, space, n as string)
end |λ|
end script
concat(map(result, ns))
end |λ|
end script
unlines(map(result, xs))
end showFloyd
-- TEST -------------------------------------------------------------
on run
showFloyd(floydN(5))
end run
-- GENERIC ABSTRACTIONS ---------------------------------------
-- concat :: [[a]] -> [a]
-- concat :: [String] -> String
on concat(xs)
set lng to length of xs
if 0 < lng and string is class of (item 1 of xs) then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to lng
set acc to acc & item i of xs
end repeat
acc
end concat
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate
-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- pred :: Int -> Int
on pred(x)
(-1) + x
end pred
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- succ :: Int -> Int
on succ(x)
1 + x
end succ
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
{{Out}}
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AutoHotkey
Floyds_triangle(row){
i = 0
loop %row%
{
n := A_Index
loop, %n%
{
m := n, j := i, i++
while (m<row)
j += m , m++
res .= spaces(StrLen(j+1)-StrLen(i) +(A_Index=1?0:1)) i
}
if (A_Index < row)
res .= "`r`n"
}
return res
}
Spaces(no){
loop, % no
res.=" "
return % res
}
Examples:
MsgBox % Floyds_triangle(14)
Outputs:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
AWK
#!/bin/awk -f
BEGIN {
if (rows !~ /^[0-9]+$/ || rows < 0) {
print "invalid rows or missing from command line"
print "syntax: awk -v rows=14 -f floyds_triangle.awk"
exit 1
}
for (row=cols=1; row<=rows; row++ cols++) {
width[row] = length(row + (rows * (rows-1))/2)
for (col=1; col<=cols; col++)
printf("%*d%c", width[col], ++n, row == col ? "\n" : " ")
}
}
output from: awk -f floyds_triangle.awk -v rows=5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
output from: awk -f floyds_triangle.awk -v rows=14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Batch File
@echo off
call:floyd 5
echo.
call:floyd 14
pause>nul
exit /b
:floyd
setlocal enabledelayedexpansion
set iterations=%1
set startn=1
set endn=1
for /l %%i in (1,1,%iterations%) do (
for /l %%j in (!startn!,1,!endn!) do (
set lastnum=%%j
set /a startn=%%j+1
)
set /a endn=!startn!+%%i
)
call:getlength %startn%
set digits=%errorlevel%
set startn=1
set endn=1
for /l %%i in (1,1,%iterations%) do (
set "line="
for /l %%j in (!startn!,1,!endn!) do (
set "space="
call:getlength %%j
set /a sparespace=%digits%-!errorlevel!
for /l %%k in (0,1,!sparespace!) do set "space=!space! "
set line=!line!!space!%%j
set /a startn=%%j+1
)
echo !line!
set /a endn=!startn!+%%i
)
exit /b
:getlength
setlocal enabledelayedexpansion
set offset=0
set string=%1
:floydloop
if "!string:~%offset%,1!"=="" endlocal && exit /b %offset%
set /a offset+=1
goto floydloop
{{out}}
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1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
BASIC
=
Applesoft BASIC
=
Line 150,160 creates a vector of the length of all entries is the last row. These values are used in line 210,220 to put the cursor at the correct horizontal position.
100 :
110 REM FLOYD'S TRIANGLE
120 :
130 DEF FN Q(A) = INT ( LOG (A) / LOG (10)) + 1
140 N = 14
150 DIM P(N): P(0) = - 1: FOR J = 1 TO N: I = (N * N - N) / 2 + J
160 P(J) = P(J - 1) + FN Q(I) + 1: NEXT J
200 FOR R = 1 TO N: FOR C = 1 TO R
210 NR = NR + 1:COL = P(C) - ( FN Q(NR) - 1)
220 HTAB COL: PRINT NR;: NEXT C
230 PRINT : NEXT R
{{out}}
]RUN
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7 8 9 10
11 12 13 14 15
]RUN
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
=
BBC BASIC
=
n = 14
num = 1
last = (n^2 - n + 2) DIV 2
FOR row = 1 TO n
col = last
FOR num = num TO num + row - 1
@% = LEN(STR$(col)) + 1 : REM set column width
PRINT num ;
col += 1
NEXT
PRINT
NEXT row
Output for n = 5:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Output for n = 14:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
==={{header|IS-BASIC}}===
=
## MasmBasic
=
'''[http://www.webalice.it/jj2006/Masm32_Tips_Tricks_and_Traps.htm Builds with Masm, UAsm or AsmC plus the MasmBasic library]'''
```MasmBasic
include \masm32\MasmBasic\MasmBasic.inc
SetGlobals rows, columns, ct, maxrows=4
Init
.Repeat
For_ rows=0 To maxrows
For_ columns=0 To rows
inc ct
Print Str$("%__i", ct)
.if columns>6
Print " "
.endif
Next
Print
Next
Print
Clr ct
add maxrows, 9 ; 4+9=13
.Until maxrows>13
Inkey
EndOfCode
{{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Befunge
0" :seniL">:#,_&>:!#@_55+,:00p::1+*2/1v
vv+1:\-1p01g5-\g00<v`*9"o"\+`"c"\`9:::_
$>>\:::9`\"c"`+\9v:>>+00g1-:00p5p1-00g^
<v\*84-\g01+`*"o"<^<<p00:+1\+1/2*+1:::\
^>:#\1#,-#:\_$$.\:#^_$$>>1+\1-55+,:!#@_
{{out}}
Lines: 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Lines: 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Bracmat
( ( floyd
= lowerLeftCorner lastInColumn lastInRow row i W w
. put$(str$("Floyd " !arg ":\n"))
& !arg*(!arg+-1)*1/2+1
: ?lowerLeftCorner
: ?lastInColumn
& 1:?lastInRow:?row:?i
& whl
' ( !row:~>!arg
& @(!lastInColumn:? [?W)
& @(!i:? [?w)
& whl'(!w+1:~>!W:?w&put$" ")
& put$!i
& ( !i:<!lastInRow
& put$" "
& 1+!lastInColumn:?lastInColumn
| put$\n
& (1+!row:?row)+!lastInRow:?lastInRow
& !lowerLeftCorner:?lastInColumn
)
& 1+!i:?i
)
)
& floyd$5
& floyd$14
);
Output:
Floyd 5:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd 14:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
C
#include <stdio.h>
void t(int n)
{
int i, j, c, len;
i = n * (n - 1) / 2;
for (len = c = 1; c < i; c *= 10, len++);
c -= i; // c is the col where width changes
#define SPEED_MATTERS 0
#if SPEED_MATTERS // in case we really, really wanted to print huge triangles often
char tmp[32], s[4096], *p;
sprintf(tmp, "%*d", len, 0);
inline void inc_numstr(void) {
int k = len;
redo: if (!k--) return;
if (tmp[k] == '9') {
tmp[k] = '0';
goto redo;
}
if (++tmp[k] == '!')
tmp[k] = '1';
}
for (p = s, i = 1; i <= n; i++) {
for (j = 1; j <= i; j++) {
inc_numstr();
__builtin_memcpy(p, tmp + 1 - (j >= c), len - (j < c));
p += len - (j < c);
*(p++) = (i - j)? ' ' : '\n';
if (p - s + len >= 4096) {
fwrite(s, 1, p - s, stdout);
p = s;
}
}
}
fwrite(s, 1, p - s, stdout);
#else // NO_IT_DOESN'T
int num;
for (num = i = 1; i <= n; i++)
for (j = 1; j <= i; j++)
printf("%*d%c", len - (j < c), num++, i - j ? ' ':'\n');
#endif
}
int main(void)
{
t(5), t(14);
// maybe not
// t(10000);
return 0;
}
Output identical to D's.
C++
#include <windows.h>
#include <sstream>
#include <iostream>
//--------------------------------------------------------------------------------------------------
using namespace std;
//--------------------------------------------------------------------------------------------------
class floyds_tri
{
public:
floyds_tri() { lastLineLen = 0; }
~floyds_tri() { killArray(); }
void create( int rows )
{
_rows = rows;
calculateLastLineLen();
display();
}
private:
void killArray()
{
if( lastLineLen )
delete [] lastLineLen;
}
void calculateLastLineLen()
{
killArray();
lastLineLen = new BYTE[_rows];
int s = 1 + ( _rows * ( _rows - 1 ) ) / 2;
for( int x = s, ix = 0; x < s + _rows; x++, ix++ )
{
ostringstream cvr;
cvr << x;
lastLineLen[ix] = static_cast<BYTE>( cvr.str().size() );
}
}
void display()
{
cout << endl << "Floyd\'s Triangle - " << _rows << " rows" << endl << "
### =========================================
" << endl;
int number = 1;
for( int r = 0; r < _rows; r++ )
{
for( int c = 0; c <= r; c++ )
{
ostringstream cvr;
cvr << number++;
string str = cvr.str();
while( str.length() < lastLineLen[c] )
str = " " + str;
cout << str << " ";
}
cout << endl;
}
}
int _rows;
BYTE* lastLineLen;
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
floyds_tri t;
int s;
while( true )
{
cout << "Enter the size of the triangle ( 0 to QUIT ): "; cin >> s;
if( !s ) return 0;
if( s > 0 ) t.create( s );
cout << endl << endl;
system( "pause" );
}
return 0;
}
//--------------------------------------------------------------------------------------------------
{{out}}
Floyd's Triangle - 5 rows
### =========================================
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd's Triangle - 14 rows
### =========================================
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
C#
{{Trans|Perl}}
using System;
using System.Text;
public class FloydsTriangle
{
internal static void Main(string[] args)
{
int count;
if (args.Length >= 1 && int.TryParse(args[0], out count) && count > 0)
{
Console.WriteLine(MakeTriangle(count));
}
else
{
Console.WriteLine(MakeTriangle(5));
Console.WriteLine();
Console.WriteLine(MakeTriangle(14));
}
}
public static string MakeTriangle(int rows)
{
int maxValue = (rows * (rows + 1)) / 2;
int digit = 0;
StringBuilder output = new StringBuilder();
for (int row = 1; row <= rows; row++)
{
for (int column = 0; column < row; column++)
{
int colMaxDigit = (maxValue - rows) + column + 1;
if (column > 0)
{
output.Append(' ');
}
digit++;
output.Append(digit.ToString().PadLeft(colMaxDigit.ToString().Length));
}
output.AppendLine();
}
return output.ToString();
}
}
Clojure
I didn't translete this, it's from my own creation.
(defn TriangleList [n]
(let [l (map inc (range))]
(loop [l l x 1 nl []]
(if (= n (count nl))
nl
(recur (drop x l) (inc x) (conj nl (take x l)))))))
(defn TrianglePrint [n]
(let [t (TriangleList n)
m (count (str (last (last t))))
f (map #(map str %) t)
l (map #(map (fn [x] (if (> m (count x))
(str (apply str (take (- m (count x))
(repeat " "))) x)
x)) %) f)
e (map #(map (fn [x] (str " " x)) %) l)]
(map #(println (apply str %)) e)))
By Average-user.
{{out}}
(TrianglePrint 5)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
(TrianglePrint 14)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
CoffeeScript
{{trans|Kotlin}}
triangle = (array) -> for n in array
console.log "#{n} rows:"
printMe = 1
printed = 0
row = 1
to_print = ""
while row <= n
cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0))
p = ("" + printMe).length
while p++ <= cols
to_print += ' '
to_print += printMe + ' '
if ++printed == row
console.log to_print
to_print = ""
row++
printed = 0
printMe++
triangle [5, 14]
Output as Kotlin.
Common Lisp
Version 1
;;;using flet to define local functions and storing precalculated column widths in array
;;;verbose, but more readable and efficient than version 2
(defun floydtriangle (rows)
(let (column-widths)
(setf column-widths (make-array rows :initial-element nil))
(flet (
(lazycat (n)
(/ (+ (expt n 2) n 2) 2))
(width (v)
(+ 1 (floor (log v 10)))))
(dotimes (i rows)
(setf (aref column-widths i)(width (+ i (lazycat (- rows 1))))))
(dotimes (row rows)
(dotimes (col (+ 1 row))
(format t "~vd " (aref column-widths col)(+ col (lazycat row))))
(format t "~%")))))
===Version 2 - any base===
;;; more concise than version 1 but less efficient for a large triangle
;;;optional "base" parameter will allow use of any base from 2 to 36
(defun floydtriangle (rows &optional (base 10))
(dotimes (row rows)
(dotimes (column (+ 1 row))
(format t "~v,vr " base (length (format nil "~vr" base (+ column (/ (+ (expt (- rows 1) 2) (- rows 1) 2) 2)))) (+ column (/ (+ (expt row 2) row 2) 2))))
(format t "~%")))
{{out}}
(floydtriangle 5)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
(floydtriangle 14)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
(floydtriangle 5 2)
1
10 11
100 101 110
111 1000 1001 1010
1011 1100 1101 1110 1111
(floydtriangle 14 36)
1
2 3
4 5 6
7 8 9 A
B C D E F
G H I J K L
M N O P Q R S
T U V W X Y Z 10
11 12 13 14 15 16 17 18 19
1A 1B 1C 1D 1E 1F 1G 1H 1I 1J
1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U
1V 1W 1X 1Y 1Z 20 21 22 23 24 25 26
27 28 29 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J
2K 2L 2M 2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X
D
import std.stdio, std.conv;
void floydTriangle(in uint n) {
immutable lowerLeftCorner = n * (n - 1) / 2 + 1;
foreach (r; 0 .. n)
foreach (c; 0 .. r + 1)
writef("%*d%c",
text(lowerLeftCorner + c).length,
r * (r + 1) / 2 + c + 1,
c == r ? '\n' : ' ');
}
void main() {
floydTriangle(5);
floydTriangle(14);
}
{{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Elixir
defmodule Floyd do
def triangle(n) do
max = trunc(n * (n + 1) / 2)
widths = for m <- (max - n + 1)..max, do: (m |> Integer.to_string |> String.length) + 1
format = Enum.map(widths, fn wide -> "~#{wide}w" end) |> List.to_tuple
line(n, 0, 1, format)
end
def line(n, n, _, _), do: :ok
def line(n, i, count, format) do
Enum.each(0..i, fn j -> :io.fwrite(elem(format,j), [count+j]) end)
IO.puts ""
line(n, i+1, count+i+1, format)
end
end
Floyd.triangle(5)
Floyd.triangle(14)
{{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Erlang
-module( floyds_triangle ).
-export( [integers/1, print/1, strings/1, task/0] ).
integers( N ) ->
lists:reverse( integers_reversed(N) ).
print( N ) ->
[io:fwrite("~s~n", [lists:flatten(X)]) || X <- strings(N)].
strings( N ) ->
Strings_reversed = [strings_from_integers(X) || X <- integers_reversed(N)],
Paddings = paddings( [lengths(X) || X <- Strings_reversed] ),
[formats(X, Y) || {X, Y} <- lists:zip(Paddings, lists:reverse(Strings_reversed))].
task() ->
print( 5 ),
print( 14 ).
formats( Paddings, Strings ) -> [lists:flatten(io_lib:format(" ~*s", [X, Y])) || {X, Y} <- lists:zip(Paddings, Strings)].
integers_reversed( N ) ->
{_End, Integers_reversed} = lists:foldl( fun integers_reversed/2, {1, []}, lists:seq(0, N - 1) ),
Integers_reversed.
integers_reversed( N, {Start, Acc} ) ->
End = Start + N,
{End + 1, [lists:seq(Start, End) | Acc]}.
lengths( Strings ) -> [string:len(X) || X <- Strings].
paddings( [Last_line | T] ) ->
{[], Paddings} = lists:foldl( fun paddings/2, {paddings_lose_last(Last_line), [Last_line]}, lists:seq(1, erlang:length(T)) ),
Paddings.
paddings( _N, {Current, Acc} ) -> {paddings_lose_last(Current), [Current | Acc]}.
paddings_lose_last( List ) ->
[_H | T] = lists:reverse( List ),
lists:reverse( T ).
strings_from_integers( Integers ) -> [erlang:integer_to_list(X) || X <- Integers].
{{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
ERRE
PROGRAM FLOYD
!
! for rosettacode.org
!
BEGIN
N=14
NUM=1
LAST=(N^2-N+2) DIV 2
FOR ROW=1 TO N DO
FOR J=1 TO ROW DO
US$=STRING$(LEN(STR$(LAST-1+J))-1,"#")
WRITE(US$;NUM;)
PRINT(" ";)
NUM+=1
END FOR
PRINT
END FOR
END PROGRAM
Example for n=14 {{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
=={{header|F_Sharp|F#}}==
open System
[<EntryPoint>]
let main argv =
// columns and rows are 0-based, so the input has to be decremented:
let maxRow =
match UInt32.TryParse(argv.[0]) with
| (true, v) when v > 0u -> int (v - 1u)
| (_, _) -> failwith "not a positive integer"
let len (n: int) = int (Math.Floor(Math.Log10(float n)))
let col0 row = row * (row + 1) / 2 + 1
let col0maxRow = col0 maxRow
for row in [0 .. maxRow] do
for col in [0 .. row] do
let value = (col0 row) + col
let pad = String(' ', (len (col0maxRow + col) - len (value) + 1))
printf "%s%d" pad value
printfn ""
0
Output for 5 and 14 (via command line argument)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
```
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Factor
```factor
USING: io kernel math math.functions math.ranges prettyprint
sequences ;
IN: rosetta-code.floyds-triangle
: floyd. ( n -- )
[ dup 1 - * 2 / 1 + dup 1 ] [ [1,b] ] bi
[
[
2dup [ log10 1 + >integer ] bi@ -
[ " " write ] times dup pprint bl [ 1 + ] bi@
] times nl [ drop dup ] dip
] each nl 3drop ;
5 14 [ floyd. ] bi@
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Forth
```forth
: lastn ( rows -- n ) dup 1- * 2/ ;
: width ( n -- n ) s>f flog ftrunc f>s 2 + ;
: triangle ( rows -- )
dup lastn 0 rot ( last 0 rows )
0 do
over cr
i 1+ 0 do
1+ swap 1+ swap
2dup width u.r
loop
drop
loop
2drop ;
```
## Fortran
Please find compilation instructions on GNU/linux system at the beginning of the source. There, also, are the example output triangles produced by running the program. The environment variable setting and command line argument are vestigial. Ignore them. The code demonstrates writing to an in memory buffer, an old feature of FORTRAN.
```FORTRAN
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Tue May 21 22:55:08
!
!a=./f && make $a && OMP_NUM_THREADS=2 $a 1223334444
!gfortran -std=f2008 -Wall -ffree-form -fall-intrinsics f.f08 -o f
! 1
! 2 3
! 4 5 6
! 7 8 9 10
! 11 12 13 14 15
!
!
! 1
! 2 3
! 4 5 6
! 7 8 9 10
! 11 12 13 14 15
! 16 17 18 19 20 21
! 22 23 24 25 26 27 28
! 29 30 31 32 33 34 35 36
! 37 38 39 40 41 42 43 44 45
! 46 47 48 49 50 51 52 53 54 55
! 56 57 58 59 60 61 62 63 64 65 66
! 67 68 69 70 71 72 73 74 75 76 77 78
! 79 80 81 82 83 84 85 86 87 88 89 90 91
! 92 93 94 95 96 97 98 99 100 101 102 103 104 105
!
!
!
!Compilation finished at Tue May 21 22:55:08
program p
integer, dimension(2) :: examples = [5, 14]
integer :: i
do i=1, size(examples)
call floyd(examples(i))
write(6, '(/)')
end do
contains
subroutine floyd(rows)
integer, intent(in) :: rows
integer :: n, i, j, k
integer, dimension(60) :: L
character(len=504) :: fmt
n = (rows*(rows+1))/2 ! Gauss's formula
do i=1,rows ! compute format of final row
L(i) = 2+int(log10(real(n-rows+i)))
end do
k = 0
do i=1,rows
do j=1,i
k = k+1
write(fmt,'(a2,i1,a1)')'(i',L(j),')'
write(6,fmt,advance='no') k
enddo
write(6,*) ''
end do
end subroutine floyd
end program p
```
## FreeBASIC
```freebasic
' version 19-09-2015
' compile with: fbc -s console
Sub pascal_triangle(n As UInteger)
Dim As UInteger a = 1, b, i, j, switch = n + 1
Dim As String frmt, frmt_1, frmt_2
' last number of the last line
i = (n * (n + 1)) \ 2
frmt_2 = String(Len(Str(i)) + 1, "#")
' first number of the last line
i = ((n - 1) * n) \ 2 + 1
frmt_1 = String(Len(Str(i)) + 1, "#")
' we have 2 different formats strings
' find the point where we have to make the switch
If frmt_1 <> frmt_2 Then
j = i + 1
While Len(Str(i)) = Len(Str(J))
j = j + 1
Wend
switch = j - i
End If
Print "output for "; Str(n) : Print
For i = 1 To n
frmt = frmt_1
b = (i * (i + 1)) \ 2
For j = a To b
' if we have the switching point change format string
If j - a = switch Then frmt = frmt_2
Print Using frmt; j;
Next j
Print
a = b + 1
Next i
Print
End Sub
' ------=< MAIN >=------
pascal_triangle(5)
pascal_triangle(14)
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
```
{{out}}
```txt
output for 5 output for 14
1 1
2 3 2 3
4 5 6 4 5 6
7 8 9 10 7 8 9 10
11 12 13 14 15 11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Gambas
'''[https://gambas-playground.proko.eu/?gist=57ab1f58785b7e07765881657e4589ab Click this link to run this code]'''
```gambas
Public Sub Main()
Dim siCount, siNo, siCounter As Short
Dim siLine As Short = 1
Dim siInput As Short[] = [5, 14]
For siCount = 0 To siInput.Max
Print "Floyd's triangle to " & siInput[siCount] & " lines"
Do
Inc siNo
Inc siCounter
Print Format(siNo, "####");
If siLine = siCounter Then
Print
Inc siLine
siCounter = 0
End If
If siLine - 1 = siInput[siCount] Then Break
Loop
siLine = 1
siCounter = 0
siNo = 0
Print
Next
End
```
Output:
```txt
Floyd's triangle to 5 lines
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd's triangle to 14 lines
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Go
```go
package main
import "fmt"
func main() {
floyd(5)
floyd(14)
}
func floyd(n int) {
fmt.Printf("Floyd %d:\n", n)
lowerLeftCorner := n*(n-1)/2 + 1
lastInColumn := lowerLeftCorner
lastInRow := 1
for i, row := 1, 1; row <= n; i++ {
w := len(fmt.Sprint(lastInColumn))
if i < lastInRow {
fmt.Printf("%*d ", w, i)
lastInColumn++
} else {
fmt.Printf("%*d\n", w, i)
row++
lastInRow += row
lastInColumn = lowerLeftCorner
}
}
}
```
{{out}}
```txt
Floyd 5:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd 14:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Haskell
'''Program'''
```haskell
import Control.Monad (liftM2)
floydTriangle =
liftM2
(zipWith (liftM2 (.) enumFromTo ((pred .) . (+))))
(scanl (+) 1)
id
[1 ..]
alignR :: Int -> Integer -> String
alignR n = (\s -> replicate (n - length s) ' ' ++ s) . show
formatFT :: Int -> IO ()
formatFT n = mapM_ (putStrLn . unwords . zipWith alignR ws) t
where
t = take n floydTriangle
ws = map (length . show) $ last t
```
'''Output''':
```haskell
*Main> formatFT 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
*Main> formatFT 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
Or, simplifying a little by delegating the recursion scheme to '''mapAccumL'''
```haskell
import Data.List (mapAccumL)
import Control.Arrow ((&&&))
floyd :: Int -> [[Int]]
floyd n =
snd $
mapAccumL
(\a x ->
((succ &&& enumFromTo a) (a + x)))
1
[0 .. pred n]
-- TEST -------------------------------------
showFloyd :: [[Int]] -> String
showFloyd xs =
let padRight n = length >>= (<$> mappend (replicate n ' ')) . drop
in unlines $
(concat .
zipWith ((. show) . padRight) ((succ . length . show) <$> last xs)) <$>
xs
main :: IO ()
main = mapM_ putStrLn $ (showFloyd . floyd) <$> [5, 14]
```
{{Out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
Or, defining just the relationship between successive terms:
```haskell
floyd :: [Int] -> [Int]
floyd xs
| n < 2 = [1]
| otherwise = [succ (div (n * pred n) 2) .. div (n * succ n) 2]
where
n = succ (length xs)
floydN :: Int -> [[Int]]
floydN n = take n (iterate floyd [1])
main :: IO ()
main = mapM_ print $ floydN 5
```
{{Out}}
```txt
[1]
[2,3]
[4,5,6]
[7,8,9,10]
[11,12,13,14,15]
```
=={{header|Icon}} and {{header|Unicon}}==
The following solution works in both languages:
```unicon
procedure main(a)
n := integer(a[1]) | 5
w := ((n*(n-1))/2)-n
c := create seq()
every row := 1 to n do {
every col := 1 to row do {
width := *(w+col)+1
every writes(right(@c,width))
}
write()
}
end
```
Sample outputs:
```txt
->ft
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
->
```
```txt
->ft 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
->
```
## J
Note: require 'strings' does nothing in J7, but is harmless (strings is already incorporated in J7).
```J
require 'strings'
floyd=: [: rplc&(' 0';' ')"1@":@(* ($ $ +/\@,)) >:/~@:i.
```
Note, the parenthesis around ($ $ +/\@,) is optional, and only included for emphasis.
Example use:
```J
floyd 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
floyd 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
How it works:
First, we create a square lower triangular matrix with our argument as the length of one side. We have 1s along the diagonal and the lower triangle, and 0s for the upper triangle.
Second, we create a running sum of these values (treating rows as being adjacent horizontally for this purpose). Then, we multiply this result by our lower triangular matrix (forcing the upper triangle to be 0s).
Then, we format the matrix as text (which gives us the required vertical alignment), and in each row we replace each space followed by a zero with two spaces.
Efficiency note: In a measurement of time used: in floyd 100, 80% the time here goes into the string manipulations -- sequential additions and multiplications are cheap. In floyd 1000 this jumps to 98% of the time. Here's a faster version (about 3x on floyd 1000) courtesy of Aai of the J forums:
```J
floyd=: [: ({.~ i.&1@E.~&' 0')"1@":@(* ($ $ +/\@,)) >:/~@:i.
```
## Java
```java
public class Floyd {
public static void main(String[] args){
printTriangle(5);
printTriangle(14);
}
private static void printTriangle(int n){
System.out.println(n + " rows:");
for(int rowNum = 1, printMe = 1, numsPrinted = 0;
rowNum <= n; printMe++){
int cols = (int)Math.ceil(Math.log10(n*(n-1)/2 + numsPrinted + 2));
System.out.printf("%"+cols+"d ", printMe);
if(++numsPrinted == rowNum){
System.out.println();
rowNum++;
numsPrinted = 0;
}
}
}
}
```
Output:
```txt
5 rows:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
14 rows:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## JavaScript
### ES5
(In a functional idiom of JavaScript)
Two main functions:
:#An expression of the Floyd triangle as a list of lists (a function of the number of rows),
:#and a mapping of that expression to a formatted string.
```JavaScript
(function () {
'use strict';
// FLOYD's TRIANGLE -------------------------------------------------------
// floyd :: Int -> [[Int]]
function floyd(n) {
return snd(mapAccumL(function (start, row) {
return [start + row + 1, enumFromTo(start, start + row)];
}, 1, enumFromTo(0, n - 1)));
};
// showFloyd :: [[Int]] -> String
function showFloyd(xss) {
var ws = map(compose([succ, length, show]), last(xss));
return unlines(map(function (xs) {
return concat(zipWith(function (w, x) {
return justifyRight(w, ' ', show(x));
}, ws, xs));
}, xss));
};
// GENERIC FUNCTIONS ------------------------------------------------------
// compose :: [(a -> a)] -> (a -> a)
function compose(fs) {
return function (x) {
return fs.reduceRight(function (a, f) {
return f(a);
}, x);
};
};
// concat :: [[a]] -> [a] | [String] -> String
function concat(xs) {
if (xs.length > 0) {
var unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
};
// enumFromTo :: Int -> Int -> [Int]
function enumFromTo(m, n) {
return Array.from({
length: Math.floor(n - m) + 1
}, function (_, i) {
return m + i;
});
};
// justifyRight :: Int -> Char -> Text -> Text
function justifyRight(n, cFiller, strText) {
return n > strText.length ? (cFiller.repeat(n) + strText)
.slice(-n) : strText;
};
// last :: [a] -> a
function last(xs) {
return xs.length ? xs.slice(-1)[0] : undefined;
};
// length :: [a] -> Int
function length(xs) {
return xs.length;
};
// map :: (a -> b) -> [a] -> [b]
function map(f, xs) {
return xs.map(f);
};
// 'The mapAccumL function behaves like a combination of map and foldl;
// it applies a function to each element of a list, passing an accumulating
// parameter from left to right, and returning a final value of this
// accumulator together with the new list.' (See hoogle )
// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
function mapAccumL(f, acc, xs) {
return xs.reduce(function (a, x) {
var pair = f(a[0], x);
return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);
};
// show ::
// (a -> String) f, Num n =>
// a -> maybe f -> maybe n -> String
var show = JSON.stringify;
// snd :: (a, b) -> b
function snd(tpl) {
return Array.isArray(tpl) ? tpl[1] : undefined;
};
// succ :: Int -> Int
function succ(x) {
return x + 1;
};
// unlines :: [String] -> String
function unlines(xs) {
return xs.join('\n');
};
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
function zipWith(f, xs, ys) {
var ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map(function (x, i) {
return f(x, ys[i]);
});
};
// TEST ( n=5 and n=14 rows ) ---------------------------------------------
return unlines(map(function (n) {
return showFloyd(floyd(n)) + '\n';
}, [5, 14]));
})();
```
{{Out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
### ES6
{{Trans|Haskell}} (mapAccumL version)
```JavaScript
(() => {
'use strict';
// FLOYD's TRIANGLE -------------------------------------------------------
// floyd :: Int -> [[Int]]
const floyd = n => snd(mapAccumL(
(start, row) => [start + row + 1, enumFromTo(start, start + row)],
1, enumFromTo(0, n - 1)
));
// showFloyd :: [[Int]] -> String
const showFloyd = xss => {
const ws = map(compose([succ, length, show]), last(xss));
return unlines(
map(xs => concat(zipWith(
(w, x) => justifyRight(w, ' ', show(x)), ws, xs
)),
xss
)
);
};
// GENERIC FUNCTIONS ------------------------------------------------------
// compose :: [(a -> a)] -> (a -> a)
const compose = fs => x => fs.reduceRight((a, f) => f(a), x);
// concat :: [[a]] -> [a] | [String] -> String
const concat = xs => {
if (xs.length > 0) {
const unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
};
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// justifyRight :: Int -> Char -> Text -> Text
const justifyRight = (n, cFiller, strText) =>
n > strText.length ? (
(cFiller.repeat(n) + strText)
.slice(-n)
) : strText;
// last :: [a] -> a
const last = xs => xs.length ? xs.slice(-1)[0] : undefined;
// length :: [a] -> Int
const length = xs => xs.length;
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f)
// 'The mapAccumL function behaves like a combination of map and foldl;
// it applies a function to each element of a list, passing an accumulating
// parameter from left to right, and returning a final value of this
// accumulator together with the new list.' (See hoogle )
// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
const mapAccumL = (f, acc, xs) =>
xs.reduce((a, x) => {
const pair = f(a[0], x);
return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);
// show ::
// (a -> String) f, Num n =>
// a -> maybe f -> maybe n -> String
const show = JSON.stringify;
// snd :: (a, b) -> b
const snd = tpl => Array.isArray(tpl) ? tpl[1] : undefined;
// succ :: Int -> Int
const succ = x => x + 1
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map((x, i) => f(x, ys[i]));
};
// TEST ( n=5 and n=14 rows ) ---------------------------------------------
return unlines(map(n => showFloyd(floyd(n)) + '\n', [5, 14]))
})();
```
{{Out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
### Spidermonkey
(Used TCL example as a starting point.)
```javascript
#!/usr/bin/env js
function main() {
print('Floyd 5:');
floyd(5);
print('\nFloyd 14:');
floyd(14);
}
function padLeft(s, w) {
for (s = String(s); s.length < w; s = ' ' + s);
return s;
}
function floyd(nRows) {
var lowerLeft = nRows * (nRows - 1) / 2 + 1;
var lowerRight = nRows * (nRows + 1) / 2;
var colWidths = [];
for (var col = lowerLeft; col <= lowerRight; col++) {
colWidths.push(String(col).length);
}
var num = 1;
for (var row = 0; row < nRows; row++) {
var line = [];
for (var col = 0; col <= row; col++, num++) {
line.push(padLeft(num, colWidths[col]));
}
print(line.join(' '));
}
}
main();
```
{{out}}
```txt
Floyd 5:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd 14:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## jq
```jq
# floyd(n) creates an n-row floyd's triangle
def floyd(n):
def lpad(len): tostring | (((len - length) * " ") + .);
# Construct an array of widths.
# Assuming N is the last integer on the last row (i.e. (n+1)*n/2),
# the last row has n entries from (1+N-n) through N:
def widths:
((n+1)*n/2) as $N
| [range(1 + $N - n; $N + 1) | tostring | length];
# emit line k assuming it starts with the integer "start"
def line(start; k; widths):
reduce range(start; start+k) as $i
(""; . + ($i|lpad(widths[$i - start])) + " ");
widths as $widths
| (reduce range(0;n) as $row
( [0, ""]; # state: i, string
(.[0] + 1) as $i | .[1] as $string
| [ ($i + $row),
($string + "\n" + line($i; $row + 1; $widths )) ] )
| .[1] ) ;
```
'''Task:'''
```jq
(5,14) | "floyd(\(.)): \(floyd(.))\n"
```
{{out}}
```sh
$ jq -M -r -n -f floyds_triangle.jq > floyds_triangle.out
floyd(5):
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
floyd(14):
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Julia
```julia
function floydtriangle(rows)
r = collect(1:div(rows *(rows + 1), 2))
spacing = Int(ceil(log10(r[end] + 1))) + 1
for i in 1:rows
for _ in 1:i
print(lpad(popfirst!(r), spacing))
end
println()
end
end
floydtriangle(5); println(); floydtriangle(14)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Kotlin
{{trans|Java}}
```scala
fun main(args: Array) = args.forEach { Triangle(it.toInt()) }
internal class Triangle(n: Int) {
init {
println("$n rows:")
var printMe = 1
var printed = 0
var row = 1
while (row <= n) {
val cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0)).toInt()
print("%${cols}d ".format(printMe))
if (++printed == row) { println(); row++; printed = 0 }
printMe++
}
}
}
```
Output as Java.
## Lasso
{{Output?|Lasso|There should only be one space between the numbers on the last row.}}
```Lasso
define floyds_triangle(n::integer) => {
local(out = array(array(1)),comp = array, num = 1)
while(#out->size < #n) => {
local(new = array)
loop(#out->last->size + 1) => {
#num++
#new->insert(#num)
}
#out->insert(#new)
}
local(pad = #out->last->last->asString->size)
with line in #out do => {
local(lineout = string)
with i in #line do => {
#i != #line->first ? #lineout->append(' ')
#lineout->append((' '*(#pad - #i->asString->size))+#i)
}
#comp->insert(#lineout)
}
return #comp->join('\r')
}
floyds_triangle(5)
'\r\r'
floyds_triangle(14)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
=={{Header|Liberty BASIC}}==
```lb
input "Number of rows needed:- "; rowsNeeded
dim colWidth(rowsNeeded) ' 5 rows implies 5 columns
for col=1 to rowsNeeded
colWidth(col) = len(str$(col + rowsNeeded*(rowsNeeded-1)/2))
next
currentNumber =1
for row=1 to rowsNeeded
for col=1 to row
print right$( " "+str$( currentNumber), colWidth(col)); " ";
currentNumber = currentNumber + 1
next
print
next
```
{{out}}
```txt
Number of rows needed:- 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Number of rows needed:- 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
=={{Header|Lua}}==
```lua
function print_floyd(rows)
local c = 1
local h = rows*(rows-1)/2
for i=1,rows do
local s = ""
for j=1,i do
for k=1, #tostring(h+j)-#tostring(c) do
s = s .. " "
end
if j ~= 1 then s = s .. " " end
s = s .. tostring(c)
c = c + 1
end
print(s)
end
end
print_floyd(5)
print_floyd(14)
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Maple
```maple
floyd := proc(rows)
local num, numRows, numInRow, i, digits;
digits := Array([]);
for i to 2 do
num := 1;
numRows := 1;
numInRow := 1;
while numRows <= rows do
if i = 2 then
printf(cat("%", digits[numInRow], "a "), num);
end if;
num := num + 1;
if i = 1 and numRows = rows then
digits(numInRow) := StringTools[Length](convert(num-1, string));
end if;
if numInRow >= numRows then
if i = 2 then
printf("\n");
end if;
numInRow := 1;
numRows := numRows + 1;
else
numInRow := numInRow +1;
end if;
end do;
end do;
return NULL;
end proc:
floyd(5);
floyd(14);
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
=={{header|Mathematica}} / {{header|Wolfram Language}}==
```Mathematica
f=Function[n,
Most/@(Range@@@Partition[FindSequenceFunction[{1,2,4,7,11}]/@Range[n+1],2,1])]
TableForm[f@5,TableAlignments->Right,TableSpacing->{1,1}]
TableForm[f@14,TableAlignments->Right,TableSpacing->{1,1}]
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
=={{header|MATLAB}} / {{header|Octave}}==
```Matlab
function floyds_triangle(n)
s = 1;
for k = 1 : n
disp(s : s + k - 1)
s = s + k;
end
```
{{out}}:
```txt
octave:22> floyds_triangle(5)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
```
=={{header|Modula-2}}==
```modula2
MODULE FloydTriangle;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteInt(n : INTEGER);
VAR buf : ARRAY[0..9] OF CHAR;
BEGIN
FormatString("%4i", buf, n);
WriteString(buf)
END WriteInt;
PROCEDURE Print(r : INTEGER);
VAR n,i,limit : INTEGER;
BEGIN
IF r<0 THEN RETURN END;
n := 1;
limit := 1;
WHILE r#0 DO
FOR i:=1 TO limit DO
WriteInt(n);
INC(n)
END;
WriteLn;
DEC(r);
INC(limit)
END
END Print;
BEGIN
Print(5);
WriteLn;
Print(14);
ReadChar
END FloydTriangle.
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## NetRexx
Both [[#REXX|REXX]] versions lend themselves very well to conversion into NetRexx programs with few changes.
### Version 1
{{Trans|REXX}}
```NetRexx
/* NetRexx */
options replace format comments java crossref symbols binary
/* REXX ***************************************************************
* 12.07.2012 Walter Pachl - translated from Python
**********************************************************************/
Parse Arg rowcount .
if rowcount.length() == 0 then rowcount = 1
say 'Rows:' rowcount
say
col = 0
len = Rexx ''
ll = '' -- last line of triangle
Loop j = rowcount * (rowcount - 1) / 2 + 1 to rowcount * (rowcount + 1) / 2
col = col + 1 -- column number
ll = ll j -- build last line
len[col] = j.length() -- remember length of column
End j
Loop i = 1 To rowcount - 1 -- now do and output the rest
ol = ''
col = 0
Loop j = i * (i - 1) / 2 + 1 to i * (i + 1) / 2 -- elements of line i
col = col + 1
ol=ol j.right(len[col]) -- element in proper length
end
Say ol -- output ith line
end i
Say ll -- output last line
```
'''Output:
```txt
Rows: 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Rows: 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
### Version 2
{{Trans|REXX}}
```NetRexx
/* NetRexx */
options replace format comments java crossref symbols binary
/*REXX program constructs & displays Floyd's triangle for any number of rows.*/
parse arg numRows .
if numRows == '' then numRows = 1 -- assume 1 row if not given
maxVal = numRows * (numRows + 1) % 2 -- calculate the max value.
say 'displaying a' numRows "row Floyd's triangle:"
say
digit = 1
loop row = 1 for numRows
col = 0
output = ''
loop digit = digit for row
col = col + 1
colMaxDigit = maxVal - numRows + col
output = output Rexx(digit).right(colMaxDigit.length())
end digit
say output
end row
```
'''Output:
```txt
displaying a 5 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
displaying a 14 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Nim
{{trans|Python}}
```nim
import strutils
proc floyd(rowcount = 5): seq[seq[int]] =
result = @[@[1]]
while result.len < rowcount:
let n = result[result.high][result.high] + 1
var row = newSeq[int]()
for i in n .. n + result[result.high].len:
row.add i
result.add row
proc pfloyd(rows: seq[seq[int]]) =
var colspace = newSeq[int]()
for n in rows[rows.high]: colspace.add(($n).len)
for row in rows:
for i, x in row:
stdout.write align($x, colspace[i])," "
echo ""
echo floyd()
for i in [5, 14]:
pfloyd(floyd(i))
echo ""
```
Output:
```txt
@[@[1], @[2, 3], @[4, 5, 6], @[7, 8, 9, 10], @[11, 12, 13, 14, 15]]
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## OCaml
```ocaml
let ( |> ) f g x = g (f x)
let rec last = function x::[] -> x | _::tl -> last tl | [] -> raise Not_found
let rec list_map2 f l1 l2 =
match (l1, l2) with
| ([], _) | (_, []) -> []
| (x::xs, y::ys) -> (f x y) :: list_map2 f xs ys
let floyd n =
let rec aux acc cur len i j =
if (List.length acc) = n then (List.rev acc) else
if j = len
then aux ((List.rev cur)::acc) [] (succ len) i 0
else aux acc (i::cur) len (succ i) (succ j)
in
aux [] [] 1 1 0
let print_floyd f =
let lens = List.map (string_of_int |> String.length) (last f) in
List.iter (fun row ->
print_endline (
String.concat " " (
list_map2 (Printf.sprintf "%*d") lens row))
) f
let () =
print_floyd (floyd (int_of_string Sys.argv.(1)))
```
## OxygenBasic
{{output?|OxygenBasic}}
```oxygenbasic
function Floyd(sys n) as string
sys i,t
for i=1 to n
t+=i
next
string s=str t
sys le=1+len s
string cr=chr(13,10)
sys lc=len cr
string buf=space(le*t+n*lc)
sys j,o,p=1
t=0
for i=1 to n
for j=1 to i
t++
s=str t
o=le-len(s)-1 'right justify
mid buf,p+o,str t
p+=le
next
mid buf,p,cr
p+=lc
next
return left buf,p-1
end function
putfile "s.txt",Floyd(5)+floyd(14)
```
## PARI/GP
{{incorrect|PARI/GP|It does not ensure that there is exactly one space between the columns in the last row.}}
```parigp
F(n)=my(fmt=Str("%"1+#Str(n*(n+1)/2)"d"),t);for(i=1,n,for(j=1,i,printf(fmt,t++));print)
F(5)
F(14)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Pascal
{{works with|Free_Pascal}}
```pascal
Program FloydDemo (input, output);
function digits(number: integer): integer;
begin
digits := trunc(ln(number) / ln(10)) + 1;
end;
procedure floyd1 (numberOfLines: integer);
{ variant with repeat .. until loop }
var
i, j, numbersInLine, startOfLastlLine: integer;
begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
j := 1;
numbersInLine := 1;
repeat
repeat
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
inc(j);
until (j > numbersInLine);
writeln;
j := 1;
inc(numbersInLine);
until (numbersInLine > numberOfLines);
end;
procedure floyd2 (numberOfLines: integer);
{ Variant with for .. do loop }
var
i, j, numbersInLine, startOfLastlLine: integer;
begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
for numbersInLine := 1 to numberOfLines do
begin
for j := 1 to numbersInLine do
begin
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
end;
writeln;
end;
end;
begin
writeln ('*** Floyd 5 ***');
floyd1(5);
writeln;
writeln ('*** Floyd 14 ***');
floyd2(14);
end.
```
Output:
```txt
% ./Floyd
*** Floyd 5 ***
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
*** Floyd 14 ***
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Perl
{{Trans|NetRexx}}
```perl
#!/usr/bin/env perl
use strict;
use warnings;
sub displayFloydTriangle {
my $numRows = shift;
print "\ndisplaying a $numRows row Floyd's triangle:\n\n";
my $maxVal = int($numRows * ($numRows + 1) / 2); # calculate the max value.
my $digit = 0;
foreach my $row (1 .. $numRows) {
my $col = 0;
my $output = '';
foreach (1 .. $row) {
++$digit;
++$col;
my $colMaxDigit = $maxVal - $numRows + $col;
$output .= sprintf " %*d", length($colMaxDigit), $digit;
}
print "$output\n";
}
return;
}
#
### = Main =============================================
my @counts;
@counts = @ARGV;
@counts = (5, 14) unless @ARGV;
foreach my $count (@counts) {
displayFloydTriangle($count);
}
0;
__END__
```
'''Output:
```txt
displaying a 5 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
displaying a 14 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Perl 6
Here's two ways of doing it.
```perl6
constant @floyd1 = (1..*).rotor(1..*);
constant @floyd2 = gather for 1..* -> $s { take [++$ xx $s] }
sub format-rows(@f) {
my @table;
my @formats = @f[@f-1].map: {"%{.chars}s"}
for @f -> @row {
@table.push: (@row Z @formats).map: -> ($i, $f) { $i.fmt($f) }
}
join "\n", @table;
}
say format-rows(@floyd1[^5]);
say '';
say format-rows(@floyd2[^14]);
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Phix
```Phix
procedure Floyds_triangle(integer n)
sequence widths = repeat(0,n)
integer k = (n * (n-1))/2
for i=1 to n do
widths[i] = sprintf("%%%dd",length(sprintf("%d",i+k))+1)
end for
k = 1
for i=1 to n do
for j=1 to i do
printf(1,widths[j],k)
k += 1
end for
printf(1,"\n")
end for
end procedure
Floyds_triangle(5)
Floyds_triangle(14)
```
{{out}}
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
```
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## PHP
```php
```
{{out}}
```txt
n = 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
n = 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## PicoLisp
### Calculate widths relative to lower left corner
```PicoLisp
(de floyd (N)
(let LLC (/ (* N (dec N)) 2)
(for R N
(for C R
(prin
(align
(length (+ LLC C))
(+ C (/ (* R (dec R)) 2)) ) )
(if (= C R) (prinl) (space)) ) ) ) )
```
===Pre-calculate all rows, and take format from last one===
```PicoLisp
(de floyd (N)
(let
(Rows
(make
(for ((I . L) (range 1 (/ (* N (inc N)) 2)) L)
(link (cut I 'L)) ) )
Fmt (mapcar length (last Rows)) )
(map inc (cdr Fmt))
(for R Rows
(apply tab R Fmt) ) ) )
```
Output in both cases:
```txt
: (floyd 5)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
: (floyd 14)
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## PL/I
```pli
(fofl, size):
floyd: procedure options (main); /* Floyd's Triangle. Wiki 12 July 2012 */
declare (i, m, n) fixed (10), (j, k, w, nr) fixed binary;
put list ('How many rows do you want?');
get list (nr); /* the number of rows */
n = nr*(nr+1)/2; /* the total number of values */
j,k = 1; m = n - nr + 1;
do i = 1 to n;
put edit (i) ( x(1), f(length(trim(m))) );
if k > 1 then do; k = k - 1; m = m + 1; end;
else do; k,j = j + 1; m = n - nr + 1; put skip; end;
end;
end floyd;
```
{{out}}
```txt
How many rows do you want?
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
How many rows do you want?
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
Final row for n=45:
991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
```
## Prolog
Works with SWI-Prolog version 6.5.3
```Prolog
floyd(N) :-
forall(between(1, N, I),
( forall(between(1,I, J),
( Last is N * (N-1)/2+J,
V is I * (I-1) /2 + J,
get_column(Last, C),
sformat(AR, '~~t~~w~~~w| ', [C]),
sformat(AF, AR, [V]),
writef(AF))),
nl)).
get_column(Last, C) :-
name(Last, N1), length(N1,C).
```
Output :
```txt
?- floyd(5).
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
true.
?- floyd(14).
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
true.
```
## PureBasic
```PureBasic
Procedure.i sumTo(n)
Protected r,i
For i=1 To n
r+i
Next
ProcedureReturn r.i
EndProcedure
; [1]
; array rsA(n)... string-lengths of the numbers
; in the bottom row
; [2]
; sumTo(i-1)+1 to sumTo(i)
; 11 12 13 14 15
; here k is the column-index for array rsA(k)
Procedure.s FloydsTriangle(n)
Protected r.s,s.s,t.s,i,j,k
; [1]
Dim rsA(n)
i=0
For j=sumTo(n-1)+1 To sumTo(n)
i+1
rsA(i)=Len(Str(j))
Next
; [2]
For i=1 To n
t.s="":k=0
For j=sumTo(i-1)+1 To sumTo(i)
k+1:t.s+RSet(Str(j),rsA(k)," ")+" "
Next
r.s+RTrim(t.s)+Chr(13)+Chr(10)
Next
r.s=Left(r.s,Len(r.s)-2)
ProcedureReturn r.s
EndProcedure
If OpenConsole()
n=5
r.s=FloydsTriangle(n)
PrintN(r.s)
n=14
r.s=FloydsTriangle(n)
PrintN(r.s)
Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
```
'''Sample Output'''
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Python
### Procedural
```python>>>
def floyd(rowcount=5):
rows = [[1]]
while len(rows) < rowcount:
n = rows[-1][-1] + 1
rows.append(list(range(n, n + len(rows[-1]) + 1)))
return rows
>>> floyd()
[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10], [11, 12, 13, 14, 15]]
>>> def pfloyd(rows=[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10]]):
colspace = [len(str(n)) for n in rows[-1]]
for row in rows:
print( ' '.join('%*i' % space_n for space_n in zip(colspace, row)))
>>> pfloyd()
1
2 3
4 5 6
7 8 9 10
>>> pfloyd(floyd(5))
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
>>> pfloyd(floyd(14))
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
>>>
```
### Functional
Using the mathematical formula for each row directly,
either in a list comprehension:
```python
def floyd(rowcount=5):
return [list(range(i * (i - 1) // 2 + 1, i * (i + 1) // 2 + 1))
for i in range(1, rowcount + 1)]
```
or in terms of concatMap:
{{Works with|Python|3}}
```python
'''Floyd triangle in terms of concatMap'''
from itertools import chain
# floyd :: Int -> [[Int]]
def floyd(n):
'''n rows of a Floyd triangle.'''
def f(i):
return [
enumFromTo(i * pred(i) // 2 + 1)(
i * succ(i) // 2
)
]
return concatMap(f)(enumFromTo(1)(n))
# main :: IO ()
def main():
'''Test'''
print(unlines(
map(str, floyd(5))
))
# GENERIC FUNCTIONS ---------------------------------------
# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))
# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
'''Concatenated list over which a function has been mapped.
The list monad can be derived by using a function f which
wraps its output in a list,
(using an empty list to represent computational failure).'''
return lambda xs: list(
chain.from_iterable(
map(f, xs)
)
)
# pred :: Enum a => a -> a
def pred(x):
'''The predecessor of a value. For numeric types, (- 1).'''
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)
# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value. For numeric types, (1 +).'''
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)
# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)
if __name__ == '__main__':
main()
```
Or alternatively, defining just the relationship between successive terms:
{{Works with|Python|3}}
```python
'''Floyd triangle in terms of iterate(f)(x)'''
from itertools import islice
# floyd :: Int -> [[Int]]
def floyd(n):
'''n rows of a Floyd triangle.'''
return take(n)(iterate(nextFloyd)([1]))
# nextFloyd :: [Int] -> [Int]
def nextFloyd(xs):
'''A Floyd triangle row derived from
the preceding row.'''
n = succ(len(xs))
return [1] if n < 2 else (
enumFromTo(succ(n * pred(n) // 2))(
n * succ(n) // 2
)
)
# showFloyd :: [[Int]] -> String
def showFloyd(xs):
'''A stringification of Floyd triangle rows.'''
return unlines(str(x) for x in xs)
# main :: IO ()
def main():
'''Test'''
print(showFloyd(
floyd(5)
))
# GENERIC ABSTRACTIONS ------------------------------------
# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated applications of f to x.'''
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)
# pred :: Enum a => a -> a
def pred(x):
'''The predecessor of a value. For numeric types, (- 1).'''
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)
# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value. For numeric types, (1 +).'''
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.'''
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)
# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)
# MAIN ----------------------------------------------------
if __name__ == '__main__':
main()
```
{{Out}}
```txt
[1]
[2, 3]
[4, 5, 6]
[7, 8, 9, 10]
[11, 12, 13, 14, 15]
```
## Racket
```racket
#lang racket
(require math)
(define (tri n)
(if (zero? n) 0 (triangle-number n)))
(define (floyd n)
(define (width x) (string-length (~a x)))
(define (~n x c) (~a x
#:width (width (+ (tri (- n 1)) 1 c))
#:align 'right #:left-pad-string " "))
(for ([r n])
(for ([c (+ r 1)])
(display (~a (~n (+ (tri r) 1 c) c) " ")))
(newline)))
(floyd 5)
(floyd 14)
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## REXX
### version 1
```rexx
/* REXX ***************************************************************
* Parse Arg rowcount
* 12.07.2012 Walter Pachl - translated from Python
**********************************************************************/
Parse Arg rowcount
col=0
ll='' /* last line of triangle */
Do j=rowcount*(rowcount-1)/2+1 to rowcount*(rowcount+1)/2
col=col+1 /* column number */
ll=ll j /* build last line */
len.col=length(j) /* remember length of column */
End
Do i=1 To rowcount-1 /* now do and output the rest */
ol=''
col=0
Do j=i*(i-1)/2+1 to i*(i+1)/2 /* elements of line i */
col=col+1
ol=ol right(j,len.col) /* element in proper length */
end
Say ol /* output ith line */
end
Say ll /* output last line */
```
Output:
```txt
n=5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
n=14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
===version 2, simple formula===
This REXX version uses a simple formula to calculate the maximum value (triangle element) displayed.
```rexx
/*REXX program constructs & displays Floyd's triangle for any number of specified rows.*/
parse arg N .; if N=='' | N=="," then N= 5 /*Not specified? Then use the default.*/
mx= N * (N+1) % 2 - N /*calculate the maximum of any value. */
say 'displaying a ' N " row Floyd's triangle:" /*show the header for Floyd's triangle.*/
say /*display a blank line below the title.*/
#=1; do r=1 for N; i= 0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i= i + 1 /*start to construct a row of triangle.*/
_= _ right(#, length( mx+i ) ) /*build a row of the Floyd's triangle. */
end /*#*/ /*calculate the max length on the fly. */
say substr(_, 2) /*remove 1st leading blank in the line.*/
end /*r*/ /*stick a fork in it, we're all done. */
```
{{out|output|text= when using the default input:}}
```txt
displaying a 5 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
```
{{out|output|text= when using the default input of: 14 }}
```txt
displaying a 14 row Floyd's triangle:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
{{out|output|text= (only showing the last row) when using the input of: 45 }}
```txt
··· 44 rows not shown ···
991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
```
===version 3, hexadecimal===
```rexx
/*REXX program constructs & displays Floyd's triangle for any number of rows in base 16.*/
parse arg N .; if N=='' | N=="," then N=6 /*Not specified? Then use the default.*/
mx=N * (N+1) % 2 - N /*calculate maximum value of any value.*/
say 'displaying a ' N " row Floyd's triangle in base 16:" /*show triangle header.*/
say
#=1; do r=1 for N; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right( d2x(#), length( d2x(mx+i))) /*build a row of the Floyd's triangle. */
end /*#*/
say substr(_, 2) /*remove 1st leading blank in the line.*/
end /*r*/ /*stick a fork in it, we're all done. */
```
{{out|output|text= when using the default input:}}
```txt
displaying a 6 row Floyd's triangle in base 16:
1
2 3
4 5 6
7 8 9 A
B C D E F
10 11 12 13 14 15
```
{{out|output|text= when using the input of: 23 }}
```txt
displaying a 23 row Floyd's triangle in base 16:
1
2 3
4 5 6
7 8 9 A
B C D E F
10 11 12 13 14 15
16 17 18 19 1A 1B 1C
1D 1E 1F 20 21 22 23 24
25 26 27 28 29 2A 2B 2C 2D
2E 2F 30 31 32 33 34 35 36 37
38 39 3A 3B 3C 3D 3E 3F 40 41 42
43 44 45 46 47 48 49 4A 4B 4C 4D 4E
4F 50 51 52 53 54 55 56 57 58 59 5A 5B
5C 5D 5E 5F 60 61 62 63 64 65 66 67 68 69
6A 6B 6C 6D 6E 6F 70 71 72 73 74 75 76 77 78
79 7A 7B 7C 7D 7E 7F 80 81 82 83 84 85 86 87 88
89 8A 8B 8C 8D 8E 8F 90 91 92 93 94 95 96 97 98 99
9A 9B 9C 9D 9E 9F A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB
AC AD AE AF B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE
BF C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF D0 D1 D2
D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF E0 E1 E2 E3 E4 E5 E6 E7
E8 E9 EA EB EC ED EE EF F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD
FE FF 100 101 102 103 104 105 106 107 108 109 10A 10B 10C 10D 10E 10F 110 111 112 113 114
```
===version 4, up to base 90===
This REXX version could be extended to even higher bases, all that is needed is to append more viewable characters to express "higher" numerals ("digits" in base '''X''').
This version of the '''base''' function has some boilerplate for signed numbers and various error checking.
```rexx
/*REXX program constructs/shows Floyd's triangle for any number of rows in any base ≤90.*/
parse arg N radx . /*obtain optional arguments from the CL*/
if N=='' | N=="," then N= 5 /*Not specified? Then use the default.*/
if radx=='' | radx=="," then radx=10 /* " " " " " " */
mx=N * (N+1) % 2 - N /*calculate maximum value of any value.*/
say 'displaying a ' N " row Floyd's triangle in base" radx':' /*display the header.*/
say
#=1; do r=1 for N; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right(base(#, radx), length( base(mx+i, radx) ) ) /*build triangle row.*/
end /*#*/
say substr(_, 2) /*remove 1st leading blank in the line,*/
end /*r*/ /* [↑] introduced by first abutment. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
base: procedure; parse arg x 1 ox,toB,inB /*obtain number, toBase, inBase. */
@abc= 'abcdefghijklmnopqrstuvwxyz' /*lowercase Latin alphabet. */
@abcU=@abc; upper @abcU /*go whole hog and extend 'em. */
@@@= '0123456789'@abc || @abcU /*prefix 'em with numeric digits.*/
@@@=@@@'<>[]{}()?~!@#$%^&*_=|\/;:¢¬≈' /*add some special chars as well.*/
/* [↑] handles up to base 90, all chars must be viewable.*/
numeric digits 3000 /*what the hey, support gihugeics*/
mxB=length(@@@) /*max base (radix) supported here*/
if toB=='' | toB=="," then toB=10 /*if skipped, assume default (10)*/
if inB=='' | inB=="," then inB=10 /* " " " " " */
if inB<2 | inb>mxB then call erb 'inBase',inB /*invalid/illegal arg: inBase. */
if toB<2 | tob>mxB then call erb 'toBase',toB /* " " " toBase. */
if x=='' then call erm /* " " " number. */
sigX=left(x, 1) /*obtain a possible leading sign.*/
if pos(sigX, '-+')\==0 then x=substr(x, 2) /*X number has a leading sign? */
else sigX= /* ··· no leading sign.*/
#=0
do j=1 for length(x); _=substr(x, j, 1) /*convert X, base inB ──► base 10*/
v=pos(_, @@@) /*get the value of this "digit". */
if v==0 | v>inB then call erd x,j,inB /*is this an illegal "numeral" ? */
#=# * inB + v - 1 /*construct new num, dig by dig. */
end /*j*/
y=
do while # >= toB /*convert #, base 10 ──► base toB*/
y=substr(@@@, (# // toB) + 1, 1)y /*construct the number for output*/
#=# % toB /* ··· and whittle # down also.*/
end /*while*/
y=sigX || substr(@@@, #+1, 1)y /*prepend the sign if it existed.*/
return y /*return the number in base toB.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
erb: call ser 'illegal' arg(2) "base: " arg(1) "must be in range: 2──► " mxB
erd: call ser 'illegal "digit" in' x":" _
erm: call ser 'no argument specified.'
ser: say; say '***error***'; say arg(1); say; exit 13
```
{{out|output|text= when using the input of: 6 2 }}
```txt
displaying a 6 row Floyd's triangle in base 2:
1
10 11
100 101 110
111 1000 1001 1010
1011 1100 1101 1110 1111
10000 10001 10010 10011 10100 10101
```
{{out|output|text= when using the input of: 23 2 }}
```txt
displaying a 12 row Floyd's triangle in base 2:
1
10 11
100 101 110
111 1000 1001 1010
1011 1100 1101 1110 1111
10000 10001 10010 10011 10100 10101
10110 10111 11000 11001 11010 11011 11100
11101 11110 11111 100000 100001 100010 100011 100100
100101 100110 100111 101000 101001 101010 101011 101100 101101
101110 101111 110000 110001 110010 110011 110100 110101 110110 110111
111000 111001 111010 111011 111100 111101 111110 111111 1000000 1000001 1000010
1000011 1000100 1000101 1000110 1000111 1001000 1001001 1001010 1001011 1001100 1001101 1001110
```
{{out|output|text= when using the input of: 40 81 }}
```txt
displaying a 40 row Floyd's triangle in base 81:
1
2 3
4 5 6
7 8 9 a
b c d e f
g h i j k l
m n o p q r s
t u v w x y z A
B C D E F G H I J
K L M N O P Q R S T
U V W X Y Z < > [ ] {
} ( ) ? ~ ! @ # $ % ^ &
* _ 10 11 12 13 14 15 16 17 18 19 1a
1b 1c 1d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o
1p 1q 1r 1s 1t 1u 1v 1w 1x 1y 1z 1A 1B 1C 1D
1E 1F 1G 1H 1I 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T
1U 1V 1W 1X 1Y 1Z 1< 1> 1[ 1] 1{ 1} 1( 1) 1? 1~ 1!
1@ 1# 1$ 1% 1^ 1& 1* 1_ 20 21 22 23 24 25 26 27 28 29
2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 2m 2n 2o 2p 2q 2r 2s
2t 2u 2v 2w 2x 2y 2z 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M
2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y 2Z 2< 2> 2[ 2] 2{ 2} 2( 2)
2? 2~ 2! 2@ 2# 2$ 2% 2^ 2& 2* 2_ 30 31 32 33 34 35 36 37 38 39 3a
3b 3c 3d 3e 3f 3g 3h 3i 3j 3k 3l 3m 3n 3o 3p 3q 3r 3s 3t 3u 3v 3w 3x
3y 3z 3A 3B 3C 3D 3E 3F 3G 3H 3I 3J 3K 3L 3M 3N 3O 3P 3Q 3R 3S 3T 3U 3V
3W 3X 3Y 3Z 3< 3> 3[ 3] 3{ 3} 3( 3) 3? 3~ 3! 3@ 3# 3$ 3% 3^ 3& 3* 3_ 40 41
42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 4g 4h 4i 4j 4k 4l 4m 4n 4o 4p 4q 4r
4s 4t 4u 4v 4w 4x 4y 4z 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M 4N 4O 4P 4Q 4R 4S
4T 4U 4V 4W 4X 4Y 4Z 4< 4> 4[ 4] 4{ 4} 4( 4) 4? 4~ 4! 4@ 4# 4$ 4% 4^ 4& 4* 4_ 50 51
52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n 5o 5p 5q 5r 5s 5t 5u
5v 5w 5x 5y 5z 5A 5B 5C 5D 5E 5F 5G 5H 5I 5J 5K 5L 5M 5N 5O 5P 5Q 5R 5S 5T 5U 5V 5W 5X 5Y
5Z 5< 5> 5[ 5] 5{ 5} 5( 5) 5? 5~ 5! 5@ 5# 5$ 5% 5^ 5& 5* 5_ 60 61 62 63 64 65 66 67 68 69 6a
6b 6c 6d 6e 6f 6g 6h 6i 6j 6k 6l 6m 6n 6o 6p 6q 6r 6s 6t 6u 6v 6w 6x 6y 6z 6A 6B 6C 6D 6E 6F 6G
6H 6I 6J 6K 6L 6M 6N 6O 6P 6Q 6R 6S 6T 6U 6V 6W 6X 6Y 6Z 6< 6> 6[ 6] 6{ 6} 6( 6) 6? 6~ 6! 6@ 6# 6$
6% 6^ 6& 6* 6_ 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 7g 7h 7i 7j 7k 7l 7m 7n 7o 7p 7q 7r 7s
7t 7u 7v 7w 7x 7y 7z 7A 7B 7C 7D 7E 7F 7G 7H 7I 7J 7K 7L 7M 7N 7O 7P 7Q 7R 7S 7T 7U 7V 7W 7X 7Y 7Z 7< 7>
7[ 7] 7{ 7} 7( 7) 7? 7~ 7! 7@ 7# 7$ 7% 7^ 7& 7* 7_ 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 8g 8h 8i
8j 8k 8l 8m 8n 8o 8p 8q 8r 8s 8t 8u 8v 8w 8x 8y 8z 8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 8K 8L 8M 8N 8O 8P 8Q 8R 8S 8T
8U 8V 8W 8X 8Y 8Z 8< 8> 8[ 8] 8{ 8} 8( 8) 8? 8~ 8! 8@ 8# 8$ 8% 8^ 8& 8* 8_ 90 91 92 93 94 95 96 97 98 99 9a 9b 9c
9d 9e 9f 9g 9h 9i 9j 9k 9l 9m 9n 9o 9p 9q 9r 9s 9t 9u 9v 9w 9x 9y 9z 9A 9B 9C 9D 9E 9F 9G 9H 9I 9J 9K 9L 9M 9N 9O 9P
9Q 9R 9S 9T 9U 9V 9W 9X 9Y 9Z 9< 9> 9[ 9] 9{ 9} 9( 9) 9? 9~ 9! 9@ 9# 9$ 9% 9^ 9& 9* 9_ a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa
```
## Ring
```ring
rows = 10
n = 0
for r = 1 to rows
for c = 1 to r
n = n + 1
see string(n) + " "
next
see nl
next
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Ruby
```ruby
def floyd(rows)
max = (rows * (rows + 1)) / 2
widths = ((max - rows + 1)..max).map {|n| n.to_s.length + 1}
n = 0
rows.times do |r|
puts (0..r).map {|i| n += 1; "%#{widths[i]}d" % n}.join
end
end
floyd(5)
floyd(14)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Run BASIC
```runbasic
input "Number of rows: "; rows
dim colSize(rows)
for col=1 to rows
colSize(col) = len(str$(col + rows * (rows-1)/2))
next
thisNum = 1
for r = 1 to rows
for col = 1 to r
print right$( " "+str$(thisNum), colSize(col)); " ";
thisNum = thisNum + 1
next
print
next
```
```txt
Number of rows: ?14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Rust
```rust
fn main() {
floyds_triangle(5);
floyds_triangle(14);
}
fn floyds_triangle(n: u32) {
let mut triangle: Vec> = Vec::new();
let mut current = 0;
for i in 1..=n {
let mut v = Vec::new();
for _ in 0..i {
current += 1;
v.push(current);
}
let row = v.iter().map(|x| x.to_string()).collect::>();
triangle.push(row);
}
for row in &triangle {
let arranged_row: Vec<_> = row
.iter()
.enumerate()
.map(|(i, number)| {
let space_len = triangle.last().unwrap()[i].len() - number.len() + 1;
let spaces = " ".repeat(space_len);
let mut padded_number = spaces;
padded_number.push_str(&number);
padded_number
})
.collect();
println!("{}", arranged_row.join(""))
}
}
```
## Scala
```scala
def floydstriangle( n:Int ) {
val s = (1 to n)
val t = s map {i => (s take(i-1) sum) + 1}
(s zip t) foreach { n =>
var m = n._2;
for( i <- 0 until n._1 ) {
val w = (t.last + i).toString.length + 1 // Column width from last row
print(" " + m takeRight w )
m+=1
}
print("\n")
}
}
// Test
floydstriangle(5)
floydstriangle(14)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Seed7
```seed7
$ include "seed7_05.s7i";
const proc: writeFloyd (in integer: rows) is func
local
var integer: number is 1;
var integer: numBeforeLastLine is 0;
var integer: line is 0;
var integer: column is 0;
begin
numBeforeLastLine := rows * pred(rows) div 2;
for line range 1 to rows do
for column range 1 to line do
if column <> 1 then
write(" ");
end if;
write(number lpad length(str(numBeforeLastLine + column)));
incr(number);
end for;
writeln;
end for;
end func;
const proc: main is func
begin
writeFloyd(5);
writeFloyd(14);
end func;
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Sidef
```ruby
func floyd(rows, n=1) {
var max = Math.range_sum(1, rows)
var widths = (max-rows .. max-1 -> map{.+n->to_s.len})
{ |r|
say %'#{1..r -> map{|i| "%#{widths[i-1]}d" % n++}.join(" ")}'
} << 1..rows
}
floyd(5) # or: floyd(5, 88)
floyd(14) # or: floyd(14, 900)
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## SPL
```spl
floyd(5)
floyd(14)
floyd(n)=
k = 0
> r, 1..n
s = ""
> j, 1..r
k += 1
f = ">"+#.upper(#.log10((n-1)*n/2+j+1)+1)+">"
s += #.str(k,f)
<
#.output(s)
<
.
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## Tcl
```tcl
proc floydTriangle n {
# Compute the column widths
for {set i [expr {$n*($n-1)/2+1}]} {$i <= $n*($n+1)/2} {incr i} {
lappend w [string length $i]
}
# Print the triangle
for {set i 0; set j 1} {$j <= $n} {incr j} {
for {set p -1; set k 0} {$k < $j} {incr k} {
puts -nonewline [format "%*d " [lindex $w [incr p]] [incr i]]
}
puts ""
}
}
# Demonstration
puts "Floyd 5:"
floydTriangle 5
puts "Floyd 14:"
floydTriangle 14
```
{{out}}
```txt
Floyd 5:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
Floyd 14:
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## TXR
```txrlisp
(defun flotri (n)
(let* ((last (trunc (* n (+ n 1)) 2))
(colw (mapcar [chain tostring length]
(range (- last n -1) last)))
(x 0))
(each ((r (range* 0 n)))
(each ((c (range 0 r)))
(format t " ~*a" [colw c] (inc x)))
(put-line))))
(defun usage (msg)
(put-line `error: @msg`)
(put-line `usage:\n@(ldiff *full-args* *args*) `)
(exit 1))
(tree-case *args*
((num blah . etc) (usage "too many arguments"))
((num) (flotri (int-str num)))
(() (usage "need an argument")))
```
{{out}}
```txt
$ txr floyds-triangle.tl
error: need an argument
usage:
txr floyds-triangle.tl
$ txr floyds-triangle.txr 1 2
error: too many arguments
usage:
txr floyds-triangle.tl
$ txr floyds-triangle.tl 5
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
$ txr floyds-triangle.tl 14
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## VBA
Solution in Microsoft Office Word. Based on VBScript
```VB
Option Explicit
Dim o As String
Sub floyd(L As Integer)
Dim r, c, m, n As Integer
n = L * (L - 1) / 2
m = 1
For r = 1 To L
o = o & vbCrLf
For c = 1 To r
o = o & Space(Len(CStr(n + c)) - Len(CStr(m))) & m & " "
m = m + 1
Next
Next
End Sub
Sub triangle()
o = "5 lines"
Call floyd(5)
o = o & vbCrLf & "14 lines"
Call floyd(14)
With Selection
.Font.Name = "Courier New"
.TypeText Text:=o
End With
End Sub
```
{{out}}
5 lines
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
14 lines
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## VBScript
{{works with|Windows Script Host|*}}
```VBScript
' Read the number of rows to use..
intRows = WScript.StdIn.ReadLine
' Get the first number of the final row so we can calculate widths...
intLastRowStart = (intRows ^ 2 - intRows) \ 2 + 1
For i = 1 To intRows
intLastRow = intLastRowStart
For j = 1 To i
k = k + 1
WScript.StdOut.Write Space(Len(intLastRow) - Len(k)) & k & " "
intLastRow = intLastRow + 1
Next
WScript.StdOut.WriteLine ""
Next
```
## Visual Basic .NET
{{trans|C#}}
```vbnet
Imports System.Text
Module Module1
Function MakeTriangle(rows As Integer) As String
Dim maxValue As Integer = (rows * (rows + 1)) / 2
Dim digit = 0
Dim output As New StringBuilder
For row = 1 To rows
For column = 0 To row - 1
Dim colMaxDigit = (maxValue - rows) + column + 1
If column > 0 Then
output.Append(" ")
End If
digit = digit + 1
output.Append(digit.ToString().PadLeft(colMaxDigit.ToString().Length))
Next
output.AppendLine()
Next
Return output.ToString()
End Function
Sub Main()
Dim args = Environment.GetCommandLineArgs()
Dim count As Integer
If args.Length > 1 AndAlso Integer.TryParse(args(1), count) AndAlso count > 0 Then
Console.WriteLine(MakeTriangle(count))
Else
Console.WriteLine(MakeTriangle(5))
Console.WriteLine()
Console.WriteLine(MakeTriangle(14))
End If
End Sub
End Module
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## XPL0
```XPL0
include c:\cxpl\codes; \include 'code' declarations
func IntLen(N); \Return number of digits in a positive integer
int N;
int I;
for I:= 1 to 20 do
[N:= N/10; if N=0 then return I];
proc Floyd(N); \Display Floyd's triangle
int N;
int M, Row, Col;
real F;
[M:= (N-1+1)*(N-1)/2; \last Floyd number on second to last row
F:= 1.0; \Floyd number counter
for Row:= 1 to N do
[for Col:= 1 to Row do
[Format(IntLen(M+Col)+1, 0); RlOut(0, F); F:= F+1.0];
CrLf(0);
];
]; \Floyd
[Floyd(5);
Floyd(14);
]
```
Output:
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## zkl
Format last line and then fit each line to that format (which is wider than terminal width before formating breaks down (at 10 digit numbers)):
```zkl
fcn lcNum(row){(row*(row+1)/2+1)} // lazy caterer's sequence
fcn floydsTriangle(rows){
fmt:=[lcNum(rows-1)..lcNum(rows)-1].pump(String,fcn(n){
String("%",n.toString().len(),"d ")}); // eg "%2d %2d %3d %3d"
foreach row in (rows){
ns:=[lcNum(row)..lcNum(row+1)-1].walk(); // eg L(4.5,6)
fmt[0,ns.len()*4].fmt(ns.xplode()).println(); // eg "%2d %2d %2d ".fmt(4,5,6)
}
}
floydsTriangle(5); println();
floydsTriangle(14);
```
{{out}}
```txt
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
## ZX Spectrum Basic
```zxbasic
10 LET n=10: LET j=1: LET col=1
20 FOR r=1 TO n
30 FOR j=j TO j+r-1
40 PRINT TAB (col);j;
50 LET col=col+3
60 NEXT j
70 PRINT
80 LET col=1
90 NEXT r
```