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{{task}}[[Category:Mathematics]] The ''[[wp:Hamming weight|population count]]'' is the number of '''1'''s (ones) in the binary representation of a non-negative integer.
''Population count'' is also known as ''pop count'', ''popcount'', ''sideways sum'', and ''Hamming weight''.
: For example, '''5''' (which is '''101''' in binary) has a population count of '''2'''.
''[http://mathworld.wolfram.com/EvilNumber.html Evil numbers]'' are non-negative integers that have an ''even'' population count.
''[http://mathworld.wolfram.com/OdiousNumber.html Odious numbers]'' are positive integers that have an ''odd'' population count.
;Task:
- write a function (or routine) to return the population count of a non-negative integer.
- all computation of the lists below should start with '''0''' (zero indexed). :* display the ''pop count'' of the 1st thirty powers of '''3''' ('''30''', '''31''', '''32''', '''33''', '''34''', ∙∙∙ '''329'''). :* display the 1st thirty ''evil'' numbers. :* display the 1st thirty ''odious'' numbers.
- display each list of integers on one line (which may or may not include a title), each set of integers being shown should be properly identified.
;See also
- The On-Line Encyclopedia of Integer Sequences: [http://oeis.org/A000069 A000069 odious numbers].
- The On-Line Encyclopedia of Integer Sequences: [http://oeis.org/A001969 A001969 evil numbers].
360 Assembly
Use of the old " Unnormalized Double Floating Point" feature, a bit forgotten, to have 56-bit integers. And also use of ICM (Insert Characters Under Mask) and TM (Test under Mask) to handle bits.
Let's note:
- in Normalized Double Floating Point, one is implemented X'4110000000000000'
- in Unnormalized Double Floating Point, one is implemented X'4E00000000000001'
* Population count 09/05/2019
POPCNT CSECT
USING POPCNT,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
SAVE (14,12) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LD F0,UN 1
STD F0,BB bb=1
MVC PG(7),=C'pow 3:' init buffer
L R10,NN nn
BCTR R10,0 nn-1
LA R9,PG+7 @pg
LA R6,0 i=0
DO WHILE=(CR,R6,LE,R10) do i=0 to nn-1
LM R0,R1,BB r0r1=bb
BAL R14,POPCOUNT call popcount(bb)
LR R1,R0 popcount(bb)
XDECO R1,XDEC edit popcount(bb)
MVC 0(3,R9),XDEC+9 output popcount(bb)
LD F0,BB bb
AW F0,BB bb*2
AW F0,BB bb*3
STD F0,BB bb=bb*3
LA R9,3(R9) @pg
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
SR R7,R7 j=0
DO WHILE=(C,R7,LE,=F'1') do j=0 to 1
MVC PG,=CL132' ' clear buffer
IF LTR,R7,Z,R7 THEN if j=0 then
MVC PG(7),=C'evil: ' init buffer
ELSE , else
MVC PG(7),=C'odious:' init buffer
ENDIF , endif
LA R9,PG+7 @pg
SR R8,R8 n=0
SR R6,R6 i=0
DO WHILE=(C,R8,LT,NN) do i=0 by 1 while(n<nn)
XR R0,R0 r0=0
LR R1,R6 r1=i
BAL R14,POPCOUNT r0=popcount(i)
SRDA R0,32 ~
D R0,=F'2' popcount(i)/2
IF CR,R0,EQ,R7 THEN if popcount(i)//2=j then
LA R8,1(R8) n=n+1
XDECO R6,XDEC edit i
MVC 0(3,R9),XDEC+9 output i
LA R9,3(R9) @pg
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
LA R7,1(R7) j++
ENDDO , enddo j
L R13,4(0,R13) restore previous savearea pointer
RETURN (14,12),RC=0 restore registers from calling sav
*------- ---- ------------------
POPCOUNT EQU * popcount(x)
ICM R0,B'1000',=X'00' zap exponant part
XR R3,R3 y=0
LA R4,56 mantissa size = 56
LOOP STC R1,CC do i=1 to 56
TM CC,X'01' if bit(x,i)=1
BNO NOTONE then{
LA R3,1(R3) y++}
NOTONE SRDA R0,1 shift right double arithmetic
BCT R4,LOOP enddo i
LR R0,R3 return(y)
BR R14 return
*------- ---- ------------------
NN DC F'30' nn=30
BB DS D bb
UN DC X'4E00000000000001' un=1 (unnormalized)
PG DC CL132' ' buffer
XDEC DS CL12 temp for xdeco
CC DS C
REGEQU
END POPCNT
{{out}}
pow 3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Ada
Specification and implementation of an auxiliary package "Population_Count". The same package is used for [[Pernicious numbers#Ada]]
with Interfaces;
package Population_Count is
subtype Num is Interfaces.Unsigned_64;
function Pop_Count(N: Num) return Natural;
end Population_Count;
package body Population_Count is
function Pop_Count(N: Num) return Natural is
use Interfaces;
K5555: constant Unsigned_64 := 16#5555555555555555#;
K3333: constant Unsigned_64 := 16#3333333333333333#;
K0f0f: constant Unsigned_64 := 16#0f0f0f0f0f0f0f0f#;
K0101: constant Unsigned_64 := 16#0101010101010101#;
X: Unsigned_64 := N;
begin
X := X - (Shift_Right(X, 1) and k5555);
X := (X and k3333) + (Shift_Right(X, 2) and k3333);
X := (X + (Shift_Right(X, 4)) and K0f0f);
X := Shift_Right((x * k0101), 56);
return Natural(X);
end Pop_Count;
end Population_Count;
The main program:
with Ada.Text_IO, Population_Count; use Ada.Text_IO; use Population_Count;
procedure Test_Pop_Count is
X: Num; use type Num;
begin
Put("Pop_Cnt(3**i):"); -- print pop_counts of powers of three
X := 1; -- X=3**0
for I in 1 .. 30 loop
Put(Natural'Image(Pop_Count(X)));
X := X * 3;
end loop;
New_Line;
Put("Evil: "); -- print first thirty evil numbers
X := 0;
for I in 1 .. 30 loop
while Pop_Count(X) mod 2 /= 0 loop -- X is not evil
X := X + 1;
end loop;
Put(Num'Image(X));
X := X + 1;
end loop;
New_Line;
Put("Odious: "); -- print thirty oudous numbers
X := 1;
for I in 1 .. 30 loop
while Pop_Count(X) mod 2 /= 1 loop -- X is not odious
X := X + 1;
end loop;
Put(Num'Image(X));
X := X + 1;
end loop;
New_Line;
end Test_Pop_Count;
{{out}}
Pop_Cnt(3**i): 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
ALGOL 68
# returns the population count (number of bits on) of the non-negative #
# integer n #
PROC population count = ( LONG INT n )INT:
BEGIN
LONG INT number := n;
INT result := 0;
WHILE number > 0 DO
IF ODD number THEN result +:= 1 FI;
number OVERAB 2
OD;
result
END # population # ;
# population count of 3^0, 3^1, 3*2, ..., 3^29 #
LONG INT power of three := 1;
print( ( "3^x pop counts:" ) );
FOR power FROM 0 TO 29 DO
print( ( " ", whole( population count( power of three ), 0 ) ) );
power of three *:= 3
OD;
print( ( newline ) );
# print the first thirty evil numbers (even population count) #
INT evil count := 0;
print( ( "evil numbers :" ) );
FOR n FROM 0 WHILE evil count < 30 DO
IF NOT ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
evil count +:= 1
FI
OD;
print( ( newline ) );
# print the first thirty odious numbers (odd population count) #
INT odious count := 0;
print( ( "odious numbers:" ) );
FOR n WHILE odious count < 30 DO
IF ODD population count( n ) THEN
print( ( " ", whole( n, 0 ) ) );
odious count +:= 1
FI
OD;
print( ( newline ) )
{{out}}
3^x pop counts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil numbers : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
ALGOL W
begin
% returns the population count (number of bits on) of the non-negative integer n %
integer procedure populationCount( integer value n ) ;
begin
integer v, count;
v := n;
count := 0;
while v > 0 do begin
if odd( v ) then count := count + 1;
v := v div 2
end while_v_gt_0 ;
count
end populationCount ;
% returns the sum of population counts of the elements of the array n %
% the bounds of n must be 1 :: length %
integer procedure arrayPopulationCount( integer array n ( * ); integer value length ) ;
begin
integer count;
count := 0;
for i := 1 until length do count := count + populationCount( n( i ) );
count
end arrayPopulationCount ;
begin %task requirements %
integer array power( 1 :: 8 );
integer n, count, carry;
% population counts of the first 30 powers of three %
% Algol W integers are 32-bit, so we simulate 64-bit with an array of integers %
% the only operation we need is multiplication by 3 %
% we use 8 bits of each number %
% start with 3^0, which is 1 %
for i := 1 until 8 do power( i ) := 0;
power( 1 ) := 1;
write( i_w := 1, s_w := 0, "3^x population: ", arrayPopulationCount( power, 8 ) );
for p := 1 until 29 do begin
carry := 0;
for b := 1 until 8 do begin
integer bValue;
bValue := ( power( b ) * 3 ) + carry;
carry := bValue div 256;
power( b ) := bValue rem 256
end for_b ;
writeon( i_w := 1, s_w := 0, " ", arrayPopulationCount( power, 8 ) )
end for_p ;
% evil numbers (even population count) %
write( "evil numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if not odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_not_odd_populationCount ;
n := n + 1
end evil_numbers_loop ;
% odious numbers (odd population count %
write( "odious numbers:" );
n := 0;
count := 0;
while count < 30 do begin
if odd( populationCount( n ) ) then begin
writeon( i_w := 1, s_w := 0, " ", n );
count := count + 1
end if_odd_populationCount ;
n := n + 1
end odious_numbers_loop
end
end.
{{out}}
3^x population: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
AppleScript
{{Trans|JavaScript}}
-- popCount :: Int -> Int
on popCount(n)
script bitSum
on |λ|(a, x)
a + (x as integer)
end |λ|
end script
foldl(bitSum, 0, characters of showIntAtBase(n, 2))
end popCount
-- TEST -----------------------------------------------------------------------
on run
script powerOfThreePopCount
on |λ|(x)
popCount(3 ^ x)
end |λ|
end script
script popCountisEven
on |λ|(x)
popCount(x) mod 2 = 0
end |λ|
end script
{popCounts:¬
map(powerOfThreePopCount, enumFromTo(0, 30)), evenThenOdd:¬
partition(popCountisEven, enumFromTo(0, 59))}
end run
-- GENERIC FUNCTIONS ----------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n 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
-- 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
-- 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
-- partition :: predicate -> List -> (Matches, nonMatches)
-- partition :: (a -> Bool) -> [a] -> ([a], [a])
on partition(f, xs)
tell mReturn(f)
set lst to {{}, {}}
repeat with x in xs
set v to contents of x
set end of item ((|λ|(v) as integer) + 1) of lst to v
end repeat
end tell
{item 2 of lst, item 1 of lst}
end partition
-- showIntAtBase :: Int -> Int -> String
on showIntAtBase(n, base)
if base > 1 then
if n > 0 then
set m to n mod base
set r to n - m
if r > 0 then
set prefix to showIntAtBase(r div base, base)
else
set prefix to ""
end if
if m < 10 then
set baseCode to 48 -- "0"
else
set baseCode to 55 -- "A" - 10
end if
prefix & character id (baseCode + m)
else
"0"
end if
else
missing value
end if
end showIntAtBase
{{Out}}
{popCounts:
{1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25},
evenThenOdd:
{{0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58},
{1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59}}}
AutoHotkey
Loop, 30
Out1 .= PopCount(3 ** (A_Index - 1)) " "
Loop, 60
i := A_Index - 1
, PopCount(i) & 0x1 ? Out3 .= i " " : Out2 .= i " "
MsgBox, % "3^x:`t" Out1 "`nEvil:`t" Out2 "`nOdious:`t" Out3
PopCount(x) { ;https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
x -= (x >> 1) & 0x5555555555555555
, x := (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
, x := (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f
return (x * 0x0101010101010101) >> 56
}
{{Output}}
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
C
{{works with|GCC}}
#include <stdio.h>
int main() {
{
unsigned long long n = 1;
for (int i = 0; i < 30; i++) {
// __builtin_popcount() for unsigned int
// __builtin_popcountl() for unsigned long
// __builtin_popcountll() for unsigned long long
printf("%d ", __builtin_popcountll(n));
n *= 3;
}
printf("\n");
}
int od[30];
int ne = 0, no = 0;
printf("evil : ");
for (int n = 0; ne+no < 60; n++) {
if ((__builtin_popcount(n) & 1) == 0) {
if (ne < 30) {
printf("%d ", n);
ne++;
}
} else {
if (no < 30) {
od[no++] = n;
}
}
}
printf("\n");
printf("odious: ");
for (int i = 0; i < 30; i++) {
printf("%d ", od[i]);
}
printf("\n");
return 0;
}
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
GCC's builtin doesn't exist prior to 3.4, and the LL version is broken in 3.4 to 4.1. In 4.2+, if the platform doesn't have a good popcount instruction or isn't enabled (e.g. not compiled with -march=native), it typically emits unoptimized code which is over 2x slower than the C below. Alternative:
#if defined(__POPCNT__) && defined(__GNUC__) && (__GNUC__> 4 || (__GNUC__== 4 && __GNUC_MINOR__> 1))
#define HAVE_BUILTIN_POPCOUNTLL
#endif
static uint64_t bitcount64(uint64_t b) {
b -= (b >> 1) & 0x5555555555555555;
b = (b & 0x3333333333333333) + ((b >> 2) & 0x3333333333333333);
b = (b + (b >> 4)) & 0x0f0f0f0f0f0f0f0f;
return (b * 0x0101010101010101) >> 56;
}
/* For 32-bit, an 8-bit table may or may not be a little faster */
static uint32_t bitcount32(uint32_t b) {
b -= (b >> 1) & 0x55555555;
b = (b & 0x33333333) + ((b >> 2) & 0x33333333);
b = (b + (b >> 4)) & 0x0f0f0f0f;
return (b * 0x01010101) >> 24;
}
C++
{{works with|C++11}}
#include <iostream>
#include <bitset>
#include <climits>
size_t popcount(unsigned long long n) {
return std::bitset<CHAR_BIT * sizeof n>(n).count();
}
int main() {
{
unsigned long long n = 1;
for (int i = 0; i < 30; i++) {
std::cout << popcount(n) << " ";
n *= 3;
}
std::cout << std::endl;
}
int od[30];
int ne = 0, no = 0;
std::cout << "evil : ";
for (int n = 0; ne+no < 60; n++) {
if ((popcount(n) & 1) == 0) {
if (ne < 30) {
std::cout << n << " ";
ne++;
}
} else {
if (no < 30) {
od[no++] = n;
}
}
}
std::cout << std::endl;
std::cout << "odious: ";
for (int i = 0; i < 30; i++) {
std::cout << od[i] << " ";
}
std::cout << std::endl;
return 0;
}
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
C#
using System;
using System.Linq;
namespace PopulationCount
{
class Program
{
private static int PopulationCount(long n)
{
string binaryn = Convert.ToString(n, 2);
return binaryn.ToCharArray().Where(t => t == '1').Count();
}
static void Main(string[] args)
{
Console.WriteLine("Population Counts:");
Console.Write("3^n : ");
int count = 0;
while (count < 30)
{
double n = Math.Pow(3f, (double)count);
int popCount = PopulationCount((long)n);
Console.Write(string.Format("{0} ", popCount));
count++;
}
Console.WriteLine();
Console.Write("Evil: ");
count = 0;
int i = 0;
while (count < 30)
{
int popCount = PopulationCount(i);
if (popCount % 2 == 0)
{
count++;
Console.Write(string.Format("{0} ", i));
}
i++;
}
Console.WriteLine();
Console.Write("Odious: ");
count = 0;
i = 0;
while (count < 30)
{
int popCount = PopulationCount(i);
if (popCount % 2 != 0)
{
count++;
Console.Write(string.Format("{0} ", i));
}
i++;
}
Console.ReadKey();
}
}
}
{{out}}
Population Counts:
3^n : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Common Lisp
(format T "3^x: ~{~a ~}~%"
(loop for i below 30
collect (logcount (expt 3 i))))
(multiple-value-bind
(evil odious)
(loop for i below 60
if (evenp (logcount i)) collect i into evil
else collect i into odious
finally (return (values evil odious)))
(format T "evil: ~{~a ~}~%" evil)
(format T "odious: ~{~a ~}~%" odious))
{{Out}}
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
D
void main() {
import std.stdio, std.algorithm, std.range, core.bitop;
enum pCount = (ulong n) => popcnt(n & uint.max) + popcnt(n >> 32);
writefln("%s\nEvil: %s\nOdious: %s",
uint.max.iota.map!(i => pCount(3L ^^ i)).take(30),
uint.max.iota.filter!(i => pCount(i) % 2 == 0).take(30),
uint.max.iota.filter!(i => pCount(i) % 2).take(30));
}
{{out}}
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
Evil: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
Odious: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Elixir
defmodule Population do
def count(n), do: count(<<n :: integer>>, 0)
defp count(<<>>, acc), do: acc
defp count(<<bit :: integer-1, rest :: bitstring>>, sum), do: count(rest, sum + bit)
def evil?(n), do: n >= 0 and rem(count(n),2) == 0
def odious?(n), do: n >= 0 and rem(count(n),2) == 1
end
IO.puts "Population count of the first thirty powers of 3:"
IO.inspect Stream.iterate(1, &(&1*3)) |> Enum.take(30) |> Enum.map(&Population.count(&1))
IO.puts "first thirty evil numbers:"
IO.inspect Stream.iterate(0, &(&1+1)) |> Stream.filter(&Population.evil?(&1)) |> Enum.take(30)
IO.puts "first thirty odious numbers:"
IO.inspect Stream.iterate(0, &(&1+1)) |> Stream.filter(&Population.odious?(&1)) |> Enum.take(30)
{{out}}
Population count of the first thirty powers of 3:
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
first thirty evil numbers:
[0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
first thirty odious numbers:
[1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Erlang
-module(population_count).
-export([popcount/1]).
-export([task/0]).
popcount(N) ->
popcount(N,0).
popcount(0,Acc) ->
Acc;
popcount(N,Acc) ->
popcount(N div 2, Acc + N rem 2).
threes(_,0,Acc) ->
lists:reverse(Acc);
threes(Threes,N,Acc) ->
threes(Threes * 3, N-1, [popcount(Threes)|Acc]).
threes(N) ->
threes(1,N,[]).
evil(_,0,Acc) ->
lists:reverse(Acc);
evil(N,Count,Acc) ->
case popcount(N) rem 2 of
0 ->
evil(N+1,Count-1,[N|Acc]);
1 ->
evil(N+1,Count,Acc)
end.
evil(Count) ->
evil(0,Count,[]).
odious(_,0,Acc) ->
lists:reverse(Acc);
odious(N,Count,Acc) ->
case popcount(N) rem 2 of
1 ->
odious(N+1,Count-1,[N|Acc]);
0 ->
odious(N+1,Count,Acc)
end.
odious(Count) ->
odious(1,Count,[]).
task() ->
io:format("Powers of 3: ~p~n",[threes(30)]),
io:format("Evil:~p~n",[evil(30)]),
io:format("Odious:~p~n",[odious(30)]).
{{out}}
population_count:task().
Powers of 3: [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,
25]
Evil:[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,
51,53,54,57,58]
Odious:[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,
50,52,55,56,59]
ok
Factor
USING: formatting kernel lists lists.lazy math math.bits
math.functions namespaces prettyprint.config sequences ;
IN: rosetta-code.population-count
: pop-count ( n -- m ) make-bits [ t = ] count ;
: 3^n ( obj -- obj' ) [ 3 swap ^ pop-count ] lmap-lazy ;
: evil ( obj -- obj' ) [ pop-count even? ] lfilter ;
: odious ( obj -- obj' ) [ pop-count odd? ] lfilter ;
: pop-count-demo ( -- )
100 margin set 0 lfrom [ 3^n ] [ evil ] [ odious ] tri
[ 30 swap ltake list>array ] tri@
"3^n: %u\nEvil: %u\nOdious: %u\n" printf ;
MAIN: pop-count-demo
{{out}}
3^n: { 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25 }
Evil: { 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58 }
Odious: { 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59 }
=={{header|Fōrmulæ}}==
In [https://wiki.formulae.org/Population_count this] page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text ([http://wiki.formulae.org/Editing_F%C5%8Drmul%C3%A6_expressions more info]). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
Forth
{{works with|Gforth|0.7.3}}
: popcnt ( n -- u) 0 swap
BEGIN dup WHILE tuck 1 AND + swap 1 rshift REPEAT
DROP ;
: odious? ( n -- t|f) popcnt 1 AND ;
: evil? ( n -- t|f) odious? 0= ;
CREATE A 30 ,
: task1 1 0 ." 3**i popcnt: "
BEGIN dup A @ < WHILE
over popcnt . 1+ swap 3 * swap
REPEAT DROP DROP CR ;
: task2 0 0 ." evil : "
BEGIN dup A @ < WHILE
over evil? IF over . 1+ THEN swap 1+ swap
REPEAT DROP DROP CR ;
: task3 0 0 ." odious : "
BEGIN dup A @ < WHILE
over odious? IF over . 1+ THEN swap 1+ swap
REPEAT DROP DROP CR ;
task1 task2 task3 BYE
{{out}}
3**i popcnt: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Fortran
{{works with|Fortran|95 and later}}
program population_count
implicit none
integer, parameter :: i64 = selected_int_kind(18)
integer(i64) :: x
integer :: i, n
x = 1
write(*, "(a8)", advance = "no") "3**i :"
do i = 1, 30
write(*, "(i3)", advance = "no") popcnt(x)
x = x * 3
end do
write(*,*)
write(*, "(a8)", advance = "no") "Evil :"
n = 0
x = 0
do while(n < 30)
if(mod(popcnt(x), 2) == 0) then
n = n + 1
write(*, "(i3)", advance = "no") x
end if
x = x + 1
end do
write(*,*)
write(*, "(a8)", advance = "no") "Odious :"
n = 0
x = 0
do while(n < 30)
if(mod(popcnt(x), 2) /= 0) then
n = n + 1
write(*, "(i3)", advance = "no") x
end if
x = x + 1
end do
contains
integer function popcnt(x)
integer(i64), intent(in) :: x
integer :: i
popcnt = 0
do i = 0, 63
if(btest(x, i)) popcnt = popcnt + 1
end do
end function
end program
{{out}}
3**i : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Free Pascal
The system unit in the RTL (run-time library) shipped with every FPC (Free Pascal compiler) distribution contains the function popCnt.
It accepts one integer parameter and is defined for all unsigned integer types.
Therefore its implementation is skipped.
program populationCount(input, output, stdErr);
var
// general advice: iterator variables are _signed_
iterator: int64;
// the variable we’d like to count the set bits in
number: qWord;
// how many evil numbers we’ve already found
evilCount: int64;
// odious numbers
odiousNumber: array[1..30] of qWord;
odiousIterator: int64;
begin
// population count for powers of three
for iterator := 0 to 29 do
begin
number := round(exp(ln(3) * iterator));
write(popCnt(number):3);
end;
writeLn();
// evil numbers
// (while preserving calculated odious numbers for next sub-task)
evilCount := 0;
odiousIterator := low(odiousNumber);
// for-loop: because we (pretend to) don’t know,
// when and where we’ve found the first 30 numbers of each
for iterator := 0 to high(iterator) do
begin
// implicit typecast: popCnt only accepts _un_-signed integers
number := iterator;
if odd(popCnt(number)) then
begin
if odiousIterator <= high(odiousNumber) then
begin
odiousNumber[odiousIterator] := number;
inc(odiousIterator);
end;
end
else
begin
if evilCount < 30 then
begin
write(number:20);
inc(evilCount);
end;
end;
if evilCount + odiousIterator > 60 then
begin
break;
end;
end;
writeLn();
// odious numbers
for number in odiousNumber do
begin
write(number:20);
end;
writeLn();
end.
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Gambas
'''[https://gambas-playground.proko.eu/?gist=538335b7b71f5ea7b59c0c82fbb0ea3e Click this link to run this code]'''
Public Sub Main()
Dim sEvil, sOdious As String 'To store the output for printing Evil and Odious
Dim iCount, iEvil, iOdious As Integer 'Counters
Print "First 30 numbers ^3\t"; 'Print title
For iCount = 0 To 29 'Count 30 times
Print Len(Replace(Bin(3 ^ iCount), "0", ""));; 'Get the Bin of the number, take out the '0's and the remaining
Next 'length is the Population count e.g. 3^2=9, Bin=1001, remove '0's='11', length=2
iCount = 0 'Reset iCount
Repeat 'Repeat/Until loop
If Even(Len(Replace(Bin(iCount), "0", ""))) Then 'If (as above) the result is Even then
sEvil &= Str(icount) & " " 'Add it to sEvil
Inc iEvil 'Increase iEvil
End If
If Odd(Len(Replace(Bin(iCount), "0", ""))) Then 'If (as above) the result is Odd then
sOdious &= Str(icount) & " " 'Add it to sOdious
Inc iOdious 'Increase iOdious
End If
Inc iCount 'Increase iCount
Until iEvil = 30 And iOdious = 30 'Until both iEvil and iOdious = 30 then exit the loop
Print "\n1st 30 Evil numbers =\t" & sEvil 'Print Evil
Print "1st 30 Odious numbers =\t" & sOdious 'Print Odious
End
Output:
First 30 numbers ^3 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
1st 30 Evil numbers = 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
1st 30 Odious numbers = 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Go
Standard Library
As of Go 1.9, this function is in the standard Library.
package main
import (
"fmt"
"math/bits"
)
func main() {
fmt.Println("Pop counts, powers of 3:")
n := uint64(1) // 3^0
for i := 0; i < 30; i++ {
fmt.Printf("%d ", bits.OnesCount64(n))
n *= 3
}
fmt.Println()
fmt.Println("Evil numbers:")
var od [30]uint64
var ne, no int
for n = 0; ne+no < 60; n++ {
if bits.OnesCount64(n)&1 == 0 {
if ne < 30 {
fmt.Printf("%d ", n)
ne++
}
} else {
if no < 30 {
od[no] = n
no++
}
}
}
fmt.Println()
fmt.Println("Odious numbers:")
for _, n := range od {
fmt.Printf("%d ", n)
}
fmt.Println()
}
{{out}}
Pop counts, powers of 3:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil numbers:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious numbers:
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Implementation
Method of WP example '''popcount_3''':
func pop64(w uint64) int {
const (
ff = 1<<64 - 1
mask1 = ff / 3
mask3 = ff / 5
maskf = ff / 17
maskp = maskf >> 3 & maskf
)
w -= w >> 1 & mask1
w = w&mask3 + w>>2&mask3
w = (w + w>>4) & maskf
return int(w * maskp >> 56)
}
Method of WP example '''popcount_4''':
func pop64(w uint64) (c int) {
for w != 0 {
w &= w - 1
c++
}
return
}
Haskell
{{works with|GHC|7.4+}}
import Data.Bits (popCount)
printPops :: (Show a, Integral a) => String -> [a] -> IO ()
printPops title counts = putStrLn $ title ++ show (take 30 counts)
main :: IO ()
main = do
printPops "popcount " $ map popCount $ iterate (*3) (1 :: Integer)
printPops "evil " $ filter (even . popCount) ([0..] :: [Integer])
printPops "odious " $ filter ( odd . popCount) ([0..] :: [Integer])
{{out}}
popcount [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25]
evil [0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58]
odious [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Or, if we want to write our own popCount, perhaps something like:
import Data.List (partition, unfoldr)
import Data.Bifoldable (biList)
import Data.Tuple (swap)
import Data.Bool (bool)
-- POPCOUNT -------------------------------------------------------------
popCount :: Int -> Int
popCount =
sum . unfoldr ((bool Nothing . Just . swap . flip quotRem 2) <*> (0 <))
-- TEST -----------------------------------------------------------------
main :: IO ()
main =
mapM_ putStrLn $
zipWith
(\k xs -> k ++ ":\n" ++ show xs ++ "\n")
["Population count of powers of 3", "evil", "odious"]
((popCount . (3 ^) <$> [0 .. 29]) :
biList (partition (even . popCount) [0 .. 59]))
{{Out}}
Population count of powers of 3:
[1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25]
evil:
[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58]
odious:
[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Idris
module Main
import Data.Vect
isOdd : (x : Int) -> Bool
isOdd x = case mod x 2 of
0 => False
1 => True
popcnt : Int -> Int
popcnt 0 = 0
popcnt x = case isOdd x of
False => popcnt (shiftR x 1)
True => 1 + popcnt (shiftR x 1)
isOdious : Int -> Bool
isOdious k = isOdd (popcnt k)
isEvil : Int -> Bool
isEvil k = not (isOdious k)
filterUnfoldN : (n : Nat) ->
(pred : Int -> Bool) -> (f : Int -> a) ->
(next : Int -> Int) -> (seed : Int) ->
Vect n a
filterUnfoldN Z pred f next seed = []
filterUnfoldN (S k) pred f next seed =
if pred seed
then (f seed) :: filterUnfoldN k pred f next (next seed)
else filterUnfoldN (S k) pred f next (next seed)
printCompact : (Show a) => Vect n a -> IO ()
printCompact v = putStrLn (unwords (map show (toList v)))
main : IO ()
main = do putStr "popcnt(3**i): "
printCompact (filterUnfoldN 30 (\_ => True) popcnt (3 *) 1)
putStr "Evil: "
printCompact (filterUnfoldN 30 isEvil id (1 +) 0)
putStr "Odious: "
printCompact (filterUnfoldN 30 isOdious id (1 +) 0)
{{Out}}
popcnt(3**i): 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
J
Implementation:
countPopln=: +/"1@#:
isOdd=: 1 = 2&|
isEven=: 0 = 2&|
Task:
countPopln 3^i.30x
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
30{.(#~ isOdd@countPopln) i. 100 NB. odd population count (aka "ODious numbers")
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
30{.(#~ isEven@countPopln) i. 100 NB. even population count (aka "EVil numbers")
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Java
import java.math.BigInteger;
public class PopCount {
public static void main(String[] args) {
{ // with int
System.out.print("32-bit integer: ");
int n = 1;
for (int i = 0; i < 20; i++) {
System.out.printf("%d ", Integer.bitCount(n));
n *= 3;
}
System.out.println();
}
{ // with long
System.out.print("64-bit integer: ");
long n = 1;
for (int i = 0; i < 30; i++) {
System.out.printf("%d ", Long.bitCount(n));
n *= 3;
}
System.out.println();
}
{ // with BigInteger
System.out.print("big integer : ");
BigInteger n = BigInteger.ONE;
BigInteger three = BigInteger.valueOf(3);
for (int i = 0; i < 30; i++) {
System.out.printf("%d ", n.bitCount());
n = n.multiply(three);
}
System.out.println();
}
int[] od = new int[30];
int ne = 0, no = 0;
System.out.print("evil : ");
for (int n = 0; ne+no < 60; n++) {
if ((Integer.bitCount(n) & 1) == 0) {
if (ne < 30) {
System.out.printf("%d ", n);
ne++;
}
} else {
if (no < 30) {
od[no++] = n;
}
}
}
System.out.println();
System.out.print("odious : ");
for (int n : od) {
System.out.printf("%d ", n);
}
System.out.println();
}
}
{{out}}
32-bit integer: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17
64-bit integer: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
big integer : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious : 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Javascript
ES6
(() => {
// popCount :: Int -> Int
const popCount = n =>
foldl(
(a, x) => a + (x === '1' ? 1 : 0),
0,
splitOn('', showIntAsBinary(n))
);
// GENERIC FUNCTIONS ------------------------------------------------------
// (++) :: [a] -> [a] -> [a]
const append = (xs, ys) => xs.concat(ys);
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// foldl :: (b -> a -> b) -> b -> [a] -> b
const foldl = (f, a, xs) => xs.reduce(f, a);
// length :: [a] -> Int
const length = xs => xs.length;
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f);
// raise :: Num -> Int -> Num
const raise = Math.pow;
// showIntAsBinary :: Int -> String
const showIntAsBinary = n => n.toString(2);
// splitOn :: String -> String -> [String]
const splitOn = (cs, xs) => xs.split(cs);
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = (p, f, x) => {
let v = x;
while (!p(v)) v = f(v);
return v;
}
// TEST -------------------------------------------------------------------
// { popCounts : [Int], evenThenOdd : ([Int], [Int]) }
return {
popCounts: map(x => popCount(raise(3, x)), enumFromTo(0, 30)),
evenThenOdd: until(
m => length(m.evenOdd[0]) >= 30 && length(m.evenOdd[1]) >= 30,
m => ({
x: m.x + 1,
evenOdd: popCount(m.x) % 2 === 0 ? (
[append(m.evenOdd[0], m.x), m.evenOdd[1]]
) : [m.evenOdd[0], append(m.evenOdd[1], m.x)]
}), {
x: 0,
evenOdd: [
[],
[]
]
}
)
.evenOdd
};
})();
{{Out}}
{"popCounts":[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25],
"evenThenOdd":[
[0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58],
[1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]]}
jq
{{works with|jq|1.4}}
def popcount:
def bin: recurse( if . == 0 then empty else ./2 | floor end ) % 2;
[bin] | add;
def firstN(count; condition):
if count > 0 then
if condition then ., (1+.| firstN(count-1; condition))
else (1+.) | firstN(count; condition)
end
else empty
end;
def task:
def pow(n): . as $m | reduce range(0;n) as $i (1; . * $m);
"The pop count of the first thirty powers of 3:",
[range(0;30) as $n | 3 | pow($n) | popcount],
"The first thirty evil numbers:",
[0 | firstN(30; (popcount % 2) == 0)],
"The first thirty odious numbers:",
[0 | firstN(30; (popcount % 2) == 1)]
;
task
{{Out}} $ jq -n -r -c -f Population_count.jq The pop count of the first thirty powers of 3: [1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25] The first thirty evil numbers: [0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58] The first thirty odious numbers: [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59]
Julia
{{works with|Julia|0.6}}
popcount(n) = sum(digits(n, 2))
println("First 3 ^ i, up to 29 pop. counts: ", join((popcount(3 ^ n) for n in 0:29), ", "))
println("Evil numbers: ", join(filter(x -> iseven(popcount(x)), 0:59), ", "))
println("Odious numbers: ", join(filter(x -> isodd(popcount(x)), 0:59), ", "))
{{out}}
First 3 ^ i, up to 29 pop. counts: 1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25
Evil numbers: 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58
Odious numbers: 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59
Kotlin
// version 1.0.6
fun popCount(n: Long) = when {
n < 0L -> throw IllegalArgumentException("n must be non-negative")
else -> java.lang.Long.bitCount(n)
}
fun main(args: Array<String>) {
println("The population count of the first 30 powers of 3 are:")
var pow3 = 1L
for (i in 1..30) {
print("${popCount(pow3)} ")
pow3 *= 3L
}
println("\n")
println("The first thirty evil numbers are:")
var count = 0
var i = 0
while (true) {
val pc = popCount(i.toLong())
if (pc % 2 == 0) {
print("$i ")
if (++count == 30) break
}
i++
}
println("\n")
println("The first thirty odious numbers are:")
count = 0
i = 1
while (true) {
val pc = popCount(i.toLong())
if (pc % 2 == 1) {
print("$i ")
if (++count == 30) break
}
i++
}
println()
}
{{out}}
The population count of the first 30 powers of 3 are:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
The first thirty evil numbers are:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
The first thirty odious numbers are:
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Lua
-- Take decimal number, return binary string
function dec2bin (n)
local bin, bit = ""
while n > 0 do
bit = n % 2
n = math.floor(n / 2)
bin = bit .. bin
end
return bin
end
-- Take decimal number, return population count as number
function popCount (n)
local bin, count = dec2bin(n), 0
for pos = 1, bin:len() do
if bin:sub(pos, pos) == "1" then count = count + 1 end
end
return count
end
-- Implement task requirements
function firstThirty (mode)
local numStr, count, n, remainder = "", 0, 0
if mode == "Evil" then remainder = 0 else remainder = 1 end
while count < 30 do
if mode == "3^x" then
numStr = numStr .. popCount(3 ^ count) .. " "
count = count + 1
else
if popCount(n) % 2 == remainder then
numStr = numStr .. n .. " "
count = count + 1
end
n = n + 1
end
end
print(mode .. ":" , numStr)
end
-- Main procedure
firstThirty("3^x")
firstThirty("Evil")
firstThirty("Odious")
{{out}}
3^x: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Mathematica
popcount[n_Integer] := IntegerDigits[n, 2] // Total
Print["population count of powers of 3"]
popcount[#] & /@ (3^Range[0, 30])
(*******)
evilQ[n_Integer] := popcount[n] // EvenQ
evilcount = 0;
evillist = {};
i = 0;
While[evilcount < 30,
If[evilQ[i], AppendTo[evillist, i]; evilcount++];
i++
]
Print["first thirty evil numbers"]
evillist
(*******)
odiousQ[n_Integer] := popcount[n] // OddQ
odiouscount = 0;
odiouslist = {};
i = 0;
While[odiouscount < 30,
If[odiousQ[i], AppendTo[odiouslist, i]; odiouscount++];
i++
]
Print["first thirty odious numbers"]
odiouslist
{{out}}
population count of powers of 3
{1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25}
first thirty evil numbers
{0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58}
first thirty odious numbers
{1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59}
min
{{works with|min|0.19.3}}
(2 over over mod 'div dip) :divmod2
(
:n () =list
(n 0 >) (n divmod2 list append #list @n) while
list (1 ==) filter size
) :pop-count
(:n 0 () (over swap append 'succ dip) n times) :iota
"3^n: " print! 30 iota (3 swap pow int pop-count) map puts!
60 iota (pop-count odd?) partition
"Evil: " print! puts! "Odious: " print! puts!
{{out}}
3^n: (1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25)
Evil: (0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58)
Odious: (1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
Oforth
: popcount(n)
0 while ( n ) [ n isOdd + n bitRight(1) ->n ] ;
: test
| i count |
30 seq map(#[ 3 swap 1- pow ]) map(#popcount) println
0 ->count
0 while( count 30 <> ) [ dup popcount isEven ifTrue: [ dup . count 1+ ->count ] 1+ ] drop printcr
0 ->count
0 while( count 30 <> ) [ dup popcount isOdd ifTrue: [ dup . count 1+ ->count ] 1+ ] drop ;
{{out}}
>test
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59 ok
PARI/GP
vector(30,n,hammingweight(3^(n-1)))
od=select(n->hammingweight(n)%2,[0..100]); ev=setminus([0..100],od);
ev[1..30]
od[1..30]
{{out}}
%1 = [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
%2 = [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
%3 = [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Pascal
{{works with|freepascal}} Like Ada a unit is used.
unit popcount;
{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,ASMCSE,CSE,PEEPHOLE}
{$Smartlink OFF}
{$ENDIF}
interface
function popcnt(n:Uint64):integer;overload;
function popcnt(n:Uint32):integer;overload;
function popcnt(n:Uint16):integer;overload;
function popcnt(n:Uint8):integer;overload;
implementation
const
//K1 = $0101010101010101;
K33 = $3333333333333333;
K55 = $5555555555555555;
KF1 = $0F0F0F0F0F0F0F0F;
KF2 = $00FF00FF00FF00FF;
KF4 = $0000FFFF0000FFFF;
KF8 = $00000000FFFFFFFF;
{
function popcnt64(n:Uint64):integer;
begin
n := n- (n shr 1) AND K55;
n := (n AND K33)+ ((n shr 2) AND K33);
n := (n + (n shr 4)) AND KF1;
n := (n*k1) SHR 56;
result := n;
end;
}
function popcnt(n:Uint64):integer;overload;
// on Intel Haswell 2x faster for fpc 32-Bit
begin
n := (n AND K55)+((n shr 1) AND K55);
n := (n AND K33)+((n shr 2) AND K33);
n := (n AND KF1)+((n shr 4) AND KF1);
n := (n AND KF2)+((n shr 8) AND KF2);
n := (n AND KF4)+((n shr 16) AND KF4);
n := (n AND KF8)+ (n shr 32);
result := n;
end;
function popcnt(n:Uint32):integer;overload;
var
c,b : NativeUint;
begin
b := n;
c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C;
c := ((b shr 2) AND NativeUint(K33));b := (b AND NativeUint(K33))+C;
c:= ((b shr 4) AND NativeUint(KF1)); b := (b AND NativeUint(KF1))+c;
c := ((b shr 8) AND NativeUint(KF2));b := (b AND NativeUint(KF2))+c;
c := b shr 16; b := (b AND NativeUint(KF4))+ C;
result := b;
end;
function popcnt(n:Uint16):integer;overload;
var
c,b : NativeUint;
begin
b := n;
c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C;
c :=((b shr 2) AND NativeUint(K33)); b := (b AND NativeUint(K33))+C;
c:= ((b shr 4) AND NativeUint(KF1)); b := (b AND NativeUint(KF1))+c;
c := b shr 8; b := (b AND NativeUint(KF2))+c;
result := b;
end;
function popcnt(n:Uint8):integer;overload;
var
c,b : NativeUint;
begin
b := n;
c := (b shr 1) AND NativeUint(K55); b := (b AND NativeUint(K55))+C;
c :=((b shr 2) AND NativeUint(K33));b := (b AND NativeUint(K33))+C;
c:= b shr 4;
result := (b AND NativeUint(KF1))+c;
end;
Begin
End.
The program
program pcntTest;
uses
sysutils,popCount;
function Odious(n:Uint32):boolean;inline;
Begin
Odious := boolean(PopCnt(n) AND 1)
end;
function EvilNumber(n:Uint32):boolean;inline;
begin
EvilNumber := boolean(NOT(PopCnt(n)) AND 1);
end;
var
s : String;
i : Uint64;
k : LongWord;
Begin
s :='PopCnt 3^i :';
i:= 1;
For k := 1 to 30 do
Begin
s := s+InttoStr(PopCnt(i)) +' ';
i := 3*i;
end;
writeln(s);writeln;
s:='Evil numbers :';i := 0;k := 0;
repeat
IF EvilNumber(i) then
Begin
inc(k);s := s+InttoStr(i) +' ';
end;
inc(i);
until k = 30;
writeln(s);writeln;s:='';
s:='Odious numbers :';i := 0;k := 0;
repeat
IF Odious(i) then
Begin
inc(k);s := s+InttoStr(i) +' ';
end;
inc(i);
until k = 30;
writeln(s);
end.
;Output:
PopCnt 3^i :1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil numbers :0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious numbers :1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Some processors define the card function, which can be used in conjunction with sets:
var
i: integer;
f: set of 0..(bitSizeOf(i)-1) absolute i; // same address as i, but different interpretation
begin
writeLn(card(f));
end;
Perl
{{trans|Perl 6}}
We'll emulate infinite lists with closures.
use strict;
use warnings;
sub population_count {
my $n = shift;
die "argument can't be negative" if $n < 0;
my $c;
for ($c = 0; $n; $n >>= 1) {
$c += $n & 1;
}
$c;
}
print join ' ', map { population_count(3**$_) } 0 .. 30 - 1;
print "\n";
sub evil {
my $i = 0;
sub { $i++ while population_count($i) % 2; $i++ }
}
sub odious {
my $i = 0;
sub { $i++ until population_count($i) % 2; $i++ }
}
my ($evil, $odious) = (evil, odious);
my (@evil, @odious);
for (1 .. 30) {
push @evil, $evil->();
push @odious, $odious->();
}
printf "Evil : %s\n", join ' ', @evil;
printf "Odious: %s\n", join ' ', @odious;
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil : 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
A faster population count can be done with pack/unpack:
Various modules can also perform a population count, with the first of these being faster than the pack/unpack builtins. The first three easily support bigints, the last will with some adjustment.
```perl
use ntheory qw/hammingweight/;
say hammingweight(1234567);
use Math::GMPz qw/Rmpz_popcount/;
say Rmpz_popcount(Math::GMPz->new(1234567));
use Math::BigInt;
say 0 + (Math::BigInt->new(1234567)->as_bin() =~ tr/1//);
use Bit::Vector;
say Bit::Vector->new_Dec(64,1234567)->Norm;
Perl 6
sub population-count(Int $n where * >= 0) { [+] $n.base(2).comb }
say map &population-count, 3 «**« ^30;
say "Evil: ", (grep { population-count($_) %% 2 }, 0 .. *)[^30];
say "Odious: ", (grep { population-count($_) % 2 }, 0 .. *)[^30];
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
That's the convenient way to write it, but the following avoids string processing and is therefore about twice as fast:
sub population-count(Int $n is copy where * >= 0) {
loop (my $c = 0; $n; $n +>= 1) {
$c += $n +& 1;
}
$c;
}
Phix
function pop_count(atom n)
if n<0 then ?9/0 end if
integer res = 0
while n!=0 do
res += and_bits(n,1)
n = floor(n/2)
end while
return res
end function
sequence s = {}
for i=0 to 29 do
s &= pop_count(power(3,i))
end for
puts(1,"3^x pop_counts:") ?s
procedure eo(integer b0, string name)
integer k=0, l=1
while l<=30 do
if and_bits(pop_count(k),1)=b0 then
s[l] = k
l += 1
end if
k += 1
end while
puts(1,name&" numbers:") ?s
end procedure
eo(0," evil")
eo(1,"odious")
{{out}}
3^x pop_counts:{1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25}
evil numbers:{0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58}
odious numbers:{1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59}
PicoLisp
(de popz (N)
(cnt
'((N) (= "1" N))
(chop (bin N)) ) )
(println
'pops:
(mapcar
'((N) (popz (** 3 N)))
(range 0 29) ) )
(setq N -1)
(println
'evil:
(make
(for (C 0 (> 30 C))
(unless (bit? 1 (popz (inc 'N)))
(link N)
(inc 'C) ) ) ) )
(setq N -1)
(println
'odio:
(make
(for (C 0 (> 30 C))
(when (bit? 1 (popz (inc 'N)))
(link N)
(inc 'C) ) ) ) )
{{out}}
pops: (1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25)
evil: (0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58)
odio: (1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
PHP
function convertToBinary($integer) {
$binary = "";
do {
$quotient = (int) ($integer / 2);
$binary .= $integer % 2;
$integer = $quotient;
} while ($quotient > 0);
return $binary;
}
function getPopCount($integer) {
$binary = convertToBinary($integer);
$offset = 0;
$popCount = 0;
do {
$pos = strpos($binary, "1", $offset);
if($pos !== FALSE) $popCount++;
$offset = $pos + 1;
} while ($pos !== FALSE);
return $popCount;
}
function print3PowPopCounts() {
for ($p = 0; $p < 30; $p++) {
echo " " . getPopCount(3 ** $p);
}
}
function printFirst30Evil() {
$counter = 0;
$pops = 0;
while ($pops < 30) {
$popCount = getPopCount($counter);
if ($popCount % 2 == 0) {
echo " " . $counter;
$pops++;
}
$counter++;
}
}
function printFirst30Odious() {
$counter = 1;
$pops = 0;
while ($pops < 30) {
$popCount = getPopCount($counter);
if ($popCount % 2 != 0) {
echo " " . $counter;
$pops++;
}
$counter++;
}
}
echo "3 ^ x pop counts:";
print3PowPopCounts();
echo "\nfirst 30 evil numbers:";
printFirst30Evil();
echo "\nfirst 30 odious numbers:";
printFirst30Odious();
{{out}}
03 ^ x pop counts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
first 30 evil numbers: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
first 30 odious numbers: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
PowerShell
function pop-count($n) {
(([Convert]::ToString($n, 2)).toCharArray() | where {$_ -eq '1'}).count
}
"pop_count 3^n: $(1..29 | foreach -Begin {$n = 1; (pop-count $n)} -Process {$n = 3*$n; (pop-count $n)} )"
"even pop_count: $($m = $n = 0; while($m -lt 30) {if(0 -eq ((pop-count $n)%2)) {$m += 1; $n}; $n += 1} )"
"odd pop_count: $($m = $n = 0; while($m -lt 30) {if(1 -eq ((pop-count $n)%2)) {$m += 1; $n}; $n += 1} )"
Output:
pop_count 3^n: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
even pop_count: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odd pop_count: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Python
Procedural
def popcount(n): return bin(n).count("1")
...
>>> [popcount(3**i) for i in range(30)]
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
>>> evil, odious, i = [], [], 0
>>> while len(evil) < 30 or len(odious) < 30:
... p = popcount(i)
... if p % 2: odious.append(i)
... else: evil.append(i)
... i += 1
...
>>> evil[:30]
[0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
>>> odious[:30]
[1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
>>>
Composition of pure functions
{{Works with|Python|3}}
'''Population count'''
from functools import reduce
# popCount :: Int -> Int
def popCount(n):
'''The count of non-zero digits in the binary
representation of the positive integer n.'''
def go(x):
return Just(divmod(x, 2)) if 0 < x else Nothing()
return sum(unfoldl(go)(n))
# TEST ----------------------------------------------------
def main():
'''Tests'''
print('Population count of first 30 powers of 3:')
print(
[popCount(pow(3, x)) for x in enumFromTo(0)(29)]
)
evilNums, odiousNums = partition(
compose(even)(popCount)
)(enumFromTo(0)(59))
print("\nFirst thirty 'evil' numbers:")
print(evilNums)
print("\nFirst thirty 'odious' numbers:")
print(odiousNums)
# GENERIC -------------------------------------------------
# Just :: a -> Maybe a
def Just(x):
'''Constructor for an inhabited Maybe (option type) value.'''
return {'type': 'Maybe', 'Nothing': False, 'Just': x}
# Nothing :: Maybe a
def Nothing():
'''Constructor for an empty Maybe (option type) value.'''
return {'type': 'Maybe', 'Nothing': True}
# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))
# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))
# even :: Int -> Bool
def even(x):
'''True if x is a
multiple of two.'''
return 0 == x % 2
# partition :: (a -> Bool) -> [a] -> ([a], [a])
def partition(p):
'''The pair of lists of those elements in xs
which respectively, do and don't
satisfy the predicate p.'''
def go(a, x):
ts, fs = a
return (ts + [x], fs) if p(x) else (ts, fs + [x])
return lambda xs: reduce(go, xs, ([], []))
# unfoldl(lambda x: Just(((x - 1), x)) if 0 != x else Nothing())(10)
# -> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
# unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
'''Dual to reduce or foldr.
Where catamorphism reduces a list to a summary value,
the anamorphic unfoldr builds a list from a seed value.
As long as f returns Just(a, b), a is prepended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.'''
def go(xr):
mb = f(xr[0])
if mb.get('Nothing'):
return []
else:
y, r = mb.get('Just')
return go((y, r)) + [r]
return lambda x: go((x, x))
# MAIN ---
if __name__ == '__main__':
main()
{{Out}}
Population count of first 30 powers of 3:
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
First thirty 'evil' numbers:
[0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
First thirty 'odious' numbers:
[1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Racket
#lang racket
;; Positive version from "popcount_4" in:
;; https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
;; negative version follows R6RS definition documented in:
;; http://docs.racket-lang.org/r6rs/r6rs-lib-std/r6rs-lib-Z-H-12.html?q=bitwise-bit#node_idx_1074
(define (population-count n)
(if (negative? n)
(bitwise-not (population-count (bitwise-not n)))
(let inr ((x n) (rv 0))
(if (= x 0) rv (inr (bitwise-and x (sub1 x)) (add1 rv))))))
(define (evil? x)
(and (not (negative? x))
(even? (population-count x))))
(define (odious? x)
(and (positive? x)
(odd? (population-count x))))
(define tasks
(list
"display the pop count of the 1st thirty powers of 3 (3^0, 3^1, 3^2, 3^3, 3^4, ...)."
(for/list ((i (in-range 30))) (population-count (expt 3 i)))
"display the 1st thirty evil numbers."
(for/list ((_ (in-range 30)) (e (sequence-filter evil? (in-naturals)))) e)
"display the 1st thirty odious numbers."
(for/list ((_ (in-range 30)) (o (sequence-filter odious? (in-naturals)))) o)))
(for-each displayln tasks)
(module+ test
(require rackunit)
(check-equal?
(for/list ((p (sequence-map population-count (in-range 16)))) p)
'(0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4))
(check-true (evil? 0) "0 has just *got* to be evil")
(check-true (evil? #b011011011) "six bits... truly evil")
(check-false (evil? #b1011011011) "seven bits, that's odd!")
(check-true (odious? 1) "the least odious number")
(check-true (odious? #b1011011011) "seven (which is odd) bits")
(check-false (odious? #b011011011) "six bits... is evil"))
{{out}}
display the pop count of the 1st thirty powers of 3 (3^0, 3^1, 3^2, 3^3, 3^4, ...).
(1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25)
display the 1st thirty evil numbers.
(0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58)
display the 1st thirty odious numbers.
(1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59)
REXX
/*REXX program counts the number of "one" bits in the binary version of a decimal number*/
/*─────────────────── and also generates a specific number of EVIL and ODIOUS numbers.*/
parse arg N B . /*get optional arguments from the C.L. */
if N=='' | N=="," then N=30 /*N not specified? Then use default. */
if B=='' | B=="," then B= 3 /*B " " " " " */
numeric digits 2000 /*be able to handle gihugeic numbers.*/
numeric digits max(20, length(B**N) ) /*whittle the precision down to size.*/
$= /* [↑] a little calculation for sizing*/
do j=0 for N; $=$ popcount(B**j) /*generate N popCounts for some powers.*/
end /*j*/ /* [↑] append popCount to the $ list. */
/* [↓] display popcounts of "3" powers*/
call showList 'popcounts of the powers of' B /*display the list with a header/title.*/
do j=0 until #>=N /*generate N evil numbers. */
if popCount(j) // 2 then iterate /*if odd population count, skip it. */
#=# + 1; $=$ j /*bump evil # count; add it to $ list.*/
end /*j*/ /* [↑] build a list of evil numbers. */
/* [↓] display the evil number list. */
call showList 'evil numbers' /*display the $ list with a header. */
do j=0 until #>=N /*generate N odious numbers. */
if popCount(j) // 2 ==0 then iterate /*if even population count, then skip. */
#=# + 1; $=$ j /*bump odious # count; add to $ list. */
end /*j*/ /* [↑] build a list of odious numbers.*/
/* [↓] display the odious number list.*/
call showList 'odious numbers' /*display the $ list with a header. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
d2b: return word( strip( x2b( d2x( arg(1) ) ), 'L', 0) 0, 1) /*dec ──► bin.*/
popCount: return length( space( translate( d2b(arg(1) ), , 0), 0) ) /*count ones. */
showList: say; say 'The 1st' N arg(1)':'; say strip($); #=0; $=; return
{{out|output|text= when using the default input:}}
The 1st 30 popcounts of the powers of 3:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
The 1st 30 evil numbers:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
The 1st 30 odious numbers:
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Ring
# Project : Population count
load "stdlib.ring"
n = 0
neven = 0
nodd = 0
binodd = []
bineven = []
binpow = []
while true
n = n + 1
numb = 0
bin = binarydigits(n)
for nr = 1 to len(bin)
if bin[nr] = "1"
numb = numb + 1
ok
next
if numb % 2 = 0
neven = neven + 1
if neven < 31
add(bineven, n)
ok
else
nodd = nodd + 1
if nodd < 31
add(binodd, n)
ok
ok
if neven > 30 and nodd > 30
exit
ok
end
see "3^x:" + nl
for n = 0 to 29
numb = 0
bin = binarydigits(pow(3,n))
for nr = 1 to len(bin)
if bin[nr] = "1"
numb = numb + 1
ok
next
add(binpow, numb)
next
showarray(binpow)
see nl
see "Evil numbers :" + nl
showarray(bineven)
see nl
see "Odious numbers:" + nl
showarray(binodd)
see nl
func showarray(vect)
see "["
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
Output:
3^x:
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
Evil numbers :
[3, 4, 5, 6, 9, 10, 12, 15, 16, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57]
Odious numbers:
[1, 2, 7, 8, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62]
Ruby
Demonstrating lazy enumerators.
class Integer
def popcount
digits(2).count(1) #pre Ruby 2.4: self.to_s(2).count("1")
end
def evil?
self >= 0 && popcount.even?
end
end
puts "Powers of 3:", (0...30).map{|n| (3**n).popcount}.join(' ')
puts "Evil:" , 0.step.lazy.select(&:evil?).first(30).join(' ')
puts "Odious:", 0.step.lazy.reject(&:evil?).first(30).join(' ')
{{Output}}
Powers of 3:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious:
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
=={{Header|Rust}}==
fn main() {
let mut num = 1u64;
let mut vec = Vec::new();
for _ in 0..30 {
vec.push(num.count_ones());
num *= 3;
}
println!("pop count of 3^0, 3^1 ... 3^29:\n{:?}",vec);
let mut even = Vec::new();
let mut odd = Vec::new();
num = 1;
while even.len() < 30 || odd.len() < 30 {
match 0 == num.count_ones()%2 {
true if even.len() < 30 => even.push(num),
false if odd.len() < 30 => odd.push(num),
_ => {}
}
num += 1;
}
println!("\nFirst 30 even pop count:\n{:?}",even);
println!("\nFirst 30 odd pop count:\n{:?}",odd);
}
{{out}}
pop count of 3^0, 3^1 ... 3^29:
[1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
First 30 even pop count:
[3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60]
First 30 odd pop count:
[1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
=={{Header|Scala}}== {{Out}}See it yourself by running in your browser either by [https://scalafiddle.io/sf/1IYuvtd/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/w0oHalRXS1mtI59tXh1NaA Scastie (remote JVM)]. {{libheader|Scala LazyList}} {{libheader|Scala Tail recursion}} {{libheader|ScalaFiddle qualified}} {{libheader|Scastie qualified}} {{works with|Scala|2.13}}
import java.lang.Long.bitCount
object PopCount extends App {
val nNumber = 30
def powersThree(start: Long): LazyList[Long] = start #:: powersThree(start * 3L)
println("Population count of 3ⁿ :")
println(powersThree(1L).map(bitCount).take(nNumber).mkString(", "))
def series(start: Long): LazyList[Long] = start #:: series(start + 1L)
println("Evil numbers:")
println(series(0L).filter(bitCount(_) % 2 == 0).take(nNumber).mkString(", "))
println("Odious numbers:")
println(series(0L).filter(bitCount(_) % 2 != 0).take(nNumber).mkString(", "))
}
Seed7
The function popcount below [http://seed7.sourceforge.net/libraries/bitset.htm#bitset(in_integer) converts]
the integer into a [http://seed7.sourceforge.net/libraries/bitset.htm bitset].
The function [http://seed7.sourceforge.net/libraries/bitset.htm#card(in_bitset) card]
is used to compute the population count of the bitset.
$ include "seed7_05.s7i";
const func integer: popcount (in integer: n) is
return card(bitset(n));
const proc: main is func
local
var integer: count is 0;
var integer: num is 0;
begin
for num range 0 to 29 do
write(popcount(3 ** num) <& " ");
end for;
writeln;
write("evil: ");
for num range 0 to integer.last until count >= 30 do
if not odd(popcount(num)) then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
write("odious: ");
count := 0;
for num range 0 to integer.last until count >= 30 do
if odd(popcount(num)) then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
end func;
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Sidef
func population_count(n) { n.as_bin.count('1') }
say "#{0..29 «**« 3 «call« population_count -> join(' ')}"
var numbers = 60.of { |i|
[i, population_count(i)]
}
say "Evil: #{numbers.grep{_[1] %% 2}.map{.first}.join(' ')}"
say "Odious: #{numbers.grep{_[1] & 1}.map{.first}.join(' ')}"
{{out}}
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Swift
func populationCount(n: Int) -> Int {
guard n >= 0 else { fatalError() }
return String(n, radix: 2).filter({ $0 == "1" }).count
}
let pows = (0...)
.lazy
.map({ Int(pow(3, Double($0))) })
.map(populationCount)
.prefix(30)
let evils = (0...)
.lazy
.filter({ populationCount(n: $0) & 1 == 0 })
.prefix(30)
let odious = (0...)
.lazy
.filter({ populationCount(n: $0) & 1 == 1 })
.prefix(30)
print("Powers:", Array(pows))
print("Evils:", Array(evils))
print("Odious:", Array(odious))
{{out}}
Powers: [1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25]
Evils: [0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58]
Odious: [1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59]
Tcl
{{works with|Tcl|8.6}}
package require Tcl 8.6
proc hammingWeight {n} {
tcl::mathop::+ {*}[split [format %llb $n] ""]
}
for {set n 0;set l {}} {$n<30} {incr n} {
lappend l [hammingWeight [expr {3**$n}]]
}
puts "p3: $l"
for {set n 0;set e [set o {}]} {[llength $e]<30||[llength $o]<30} {incr n} {
lappend [expr {[hammingWeight $n]&1 ? "o" : "e"}] $n
}
puts "evil: [lrange $e 0 29]"
puts "odious: [lrange $o 0 29]"
{{out}}
p3: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
UNIX Shell
{{works with|bash}}
popcount() {
local -i n=$1
(( n < 0 )) && return 1
local ones=0
while (( n > 0 )); do
(( ones += n%2 ))
(( n /= 2 ))
done
echo $ones
}
popcount_3s=()
n=1
for (( i=0; i<30; i++ )); do
popcount_3s+=( $(popcount $n) )
(( n *= 3 ))
done
echo "powers of 3 popcounts: ${popcount_3s[*]}"
evil=()
odious=()
n=0
while (( ${#evil[@]} < 30 || ${#odious[@]} < 30 )); do
p=$( popcount $n )
if (( $p%2 == 0 )); then
evil+=( $n )
else
odious+=( $n )
fi
(( n++ ))
done
echo "evil nums: ${evil[*]:0:30}"
echo "odious nums: ${odious[*]:0:30}"
{{output}}
powers of 3 popcounts: 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil nums: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious nums: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
VBA
{{trans|VBScript}} {{works with|VBA|VBA Excel 2013}} The Decimal subtype of Variant does the job to expand 32-bit integers (Long) to 28-digit integers (Decimal).
Sub Population_count()
nmax = 30
b = 3
n = 0: List = "": bb = 1
For i = 0 To nmax - 1
List = List & " " & popcount(bb)
bb = bb * b
Next 'i
Debug.Print "popcounts of the powers of " & b
Debug.Print List
For j = 0 To 1
If j = 0 Then c = "evil numbers" Else c = "odious numbers"
n = 0: List = "": i = 0
While n < nmax
If (popcount(i) Mod 2) = j Then
n = n + 1
List = List & " " & i
End If
i = i + 1
Wend
Debug.Print c
Debug.Print List
Next 'j
End Sub 'Population_count
Private Function popcount(x)
Dim y, xx, xq, xr
xx = x
While xx > 0
xq = Int(xx / 2)
xr = xx - xq * 2
If xr = 1 Then y = y + 1
xx = xq
Wend
popcount = y
End Function 'popcount
{{out}}
popcounts of the powers of 3:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil numbers:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious numbers:
' 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
VBScript
Use of the variant currency subtype. Currency mode is a gray area where some operators do not work, for instance: ^ \ Mod
' Population count - VBScript - 10/05/2019
nmax=30
b=3
n=0: list="": bb=1
For i=0 To nmax-1
list=list & " " & popcount(bb)
bb=bb*b
Next 'i
Msgbox list,,"popcounts of the powers of " & b
For j=0 to 1
If j=0 Then c="evil numbers": Else c="odious numbers"
n=0: list="": i=0
While n<nmax
If (popcount(i) Mod 2)=j Then
n=n+1
list=list & " " & i
End If
i=i+1
Wend
Msgbox list,,c
Next 'j
Function popcount(x)
Dim y,xx,xq,xr
xx=x
While xx>0
xq=Int(xx/2)
xr=xx-xq*2
If xr=1 Then y=y+1
xx=xq
Wend
popcount=y
End Function 'popcount
{{out}}
popcounts of the powers of 3:
1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
evil numbers:
0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
odious numbers:
1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Visual Basic .NET
{{trans|C#}}
Module Module1
Function PopCnt(ByVal n As Long) As Integer
Return Convert.ToString(n, 2).ToCharArray().Where(Function(x) x = "1").Count()
End Function
Sub Aline(ByVal a As List(Of Integer), ByVal title As String)
Console.WriteLine("{0, -8}{1}", title, String.Join(" ", a.Take(30)))
End Sub
Sub Main(ByVal args As String())
Console.WriteLine("Population Counts:")
Dim t As New List(Of Integer), e As New List(Of Integer), o As New List(Of Integer)
For count As Integer = 0 To 99
If PopCnt(count) Mod 2 = 0 Then e.Add(count) Else o.Add(count)
If count < 30 Then t.Add(PopCnt(Math.Pow(3, count)))
Next
Aline(t, "3^n :") : Aline(e, "Evil:") : Aline(o, "Odious:")
''' Extra:
Dim eo As Boolean = e.Contains(0), res As String = "", i As Integer = 0
e.Add(0) : o.Add(0)
Do
If eo Then
If e(i + 1) = e(i) + 1 Then
res += "͞ " : i += 1
ElseIf o(i) = e(i) + 1 Then
res += "↓" : eo = Not eo
Else
res += "\" : eo = Not eo : i += 1
End If
Else
If o(i + 1) = o(i) + 1 Then
res += "͢ " : i += 1
ElseIf e(i) = o(i) + 1 Then
res += "↑" : eo = Not eo
Else
res += "/" : eo = Not eo : i += 1
End If
End If
Loop Until i >= e.Count - 1
Console.WriteLine(vbLf & "Pattern:{0}", res.Substring(0, res.Count() - 1))
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module
{{out}} Added a "Pattern" line. Not quite getting the arrows I wanted, but the "Pattern" line shows the sequence pattern of integers for the Evil and Odious output. The pattern goes to about 50, whereas only the first 30 Evil and Odious integers are shown.
Population Counts:
3^n : 1 2 2 4 3 6 6 5 6 8 9 13 10 11 14 15 11 14 14 17 17 20 19 22 16 18 24 30 25 25
Evil: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30 33 34 36 39 40 43 45 46 48 51 53 54 57 58
Odious: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31 32 35 37 38 41 42 44 47 49 50 52 55 56 59
Pattern:↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑\↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓/↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑\↑͞ ↓/↓͢ ↑͞ ↓͢ ↑\↑͞ ↓/↓͢ ↑\↑͞ ↓͢ ↑͞ ↓/↓͢ ↑͞ ↓͢ ↑
'''P.S.''', The underscore-right-arrows and overscore characters on the Pattern line may not appear properly on some browsers.
Yabasic
print "Pop count (3^x): "
for i = 0 to 29
print population(3^i);
next
print "\n"
print "Evil: "
EvilOdious(30)
print "\n"
print "Odious: "
EvilOdious(30, 1)
print "\n"
sub EvilOdious(limit, type)
local i, count, eo
repeat
eo = mod(population(i), 2)
if (type and eo) or (not type and not eo) count = count + 1 : print i;
i = i + 1
until(count = limit)
end sub
sub population(number)
local i, binary$, popul
binary$ = bin$(number)
for i = 1 to len(binary$)
popul = popul + val(mid$(binary$, i, 1))
next
return popul
end sub
zkl
Ints have the 1s count as a property.
n:=1; do(30){ print(n.num1s,","); n*=3 } println();
println("evil: ",[0..].filter(30,fcn(n){ n.num1s.isEven }).concat(","));
// now, as an iterator aka lazy:
println("odious: ",(0).walker(*).tweak( // 0,1,2,3,4... iterator
fcn(n){ if(n.num1s.isEven) Void.Skip else n }).walk(30).concat(","));
{{out}}
1,2,2,4,3,6,6,5,6,8,9,13,10,11,14,15,11,14,14,17,17,20,19,22,16,18,24,30,25,25,
evil: 0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58
odious: 1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59