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{{task}} The numerical rank of competitors in a competition shows if one is better than, equal to, or worse than another based on their results in a competition.
The numerical rank of a competitor can be assigned in several [[wp:Ranking|different ways]].
;Task: The following scores are accrued for all competitors of a competition (in best-first order):
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
For each of the following ranking methods, create a function/method/procedure/subroutine... that applies the ranking method to an ordered list of scores with scorers:
Standard. (Ties share what would have been their first ordinal number).
Modified. (Ties share what would have been their last ordinal number).
Dense. (Ties share the next available integer).
Ordinal. ((Competitors take the next available integer. Ties are not treated otherwise).
Fractional. (Ties share the mean of what would have been their ordinal numbers).
See the [[wp:Ranking|wikipedia article]] for a fuller description.
Show here, on this page, the ranking of the test scores under each of the numbered ranking methods.
AutoHotkey
Rank(data, opt:=1){ ; opt = 1 Standard (default), 2 Modified, 3 Dense, 4 Ordinal, 5 Fractional
for index, val in StrSplit(data, "`n", "`r") {
RegExMatch(val, "^(\d+)\s+(.*)", Match)
if !(Match1=prev)
n := index
prev := Match1
Res1 .= n "`t" Match "`n"
Res4 .= index "`t" Match "`n"
Temp .= n ":" index " " Match "`n"
}
n:=0
while pos := RegExMatch(Temp, "`asm)^(\d+).*?\R(?!\1)|.+", Match, pos?pos+StrLen(Match):1) {
n += StrSplit(Trim(Match, "`r`n"), "`n", "`r").MaxIndex()
Res2 .= RegExReplace(Match, "`am)^\d+:\d+", n "`t")
Res3 .= RegExReplace(Match, "`am)^\d+:\d+", A_Index "`t")
R := 0
for index, val in StrSplit(Match, "`n", "`r")
R += StrSplit(val, ":").2
Res5 .= RegExReplace(Match, "`am)^\d+:\d+", RegExReplace(R / StrSplit(Trim(Match, "`r`n"), "`n", "`r").MaxIndex(), "\.?0+$") "`t")
}
return Res%opt%
}
Example:
data =
(
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
)
MsgBox, 262144, ,% ""
. "Standard Ranking:`n" Rank(data)
. "`nModified Ranking:`n" Rank(data, 2)
. "`nDense Ranking:`n" Rank(data, 3)
. "`nOrdinal Ranking:`n" Rank(data, 4)
. "`nFractional Ranking:`n" Rank(data, 5)
return
Output:
Standard Ranking:
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified Ranking:
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense Ranking:
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal Ranking:
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional Ranking:
1 44 Solomon
2.5 42 Jason
2.5 42 Errol
5 41 Garry
5 41 Bernard
5 41 Barry
7 39 Stephen
AWK
{{trans|Python}} This uses separate files for each method of ranking:
##
## Dense ranking in file: ranking_d.awk
##
BEGIN{ lastresult = "!"; lastrank = 0 }
function d_rank(){
if($1==lastresult){
print lastrank, $0
}else{
lastresult = $1
print ++lastrank, $0 }
}
//{d_rank() }
##
## Fractional ranking in file: ranking_f.awk
##
BEGIN{
last = "!"
flen = 0 }
function f_rank(){
item = $0
if($1!=last){
if(flen){
sum = 0
for(fl=0; fl < flen;){
$0 = fifo[fl++]
sum += $1 }
mean = sum / flen
for(fl=0; fl < flen;){
$0 = fifo[fl++]
$1 = ""
printf("%3g %s\n", mean, $0) }
flen = 0
}}
$0 = item
last = $1
fifo[flen++] = sprintf("%i %s", FNR, item)
}
//{f_rank()}
END{ if(flen){
sum = 0
for(fl=0; fl < flen;){
$0 = fifo[fl++]
sum += $1 }
mean = sum / flen
for(fl=0; fl < flen;){
$0 = fifo[fl++]
$1 = ""
printf("%3g %s\n", mean, $0) }}}
##
## Modified competition ranking in file: ranking_mc.awk
##
BEGIN{
lastresult = "!"
flen = 0 }
function mc_rank(){
if($1==lastresult){
fifo[flen++] = $0
}else{
for(fl=0; fl < flen;){
print FNR-1, fifo[fl++]}
flen = 0
fifo[flen++] = $0
lastresult = $1}
}
//{mc_rank()}
END{ for(fl=0; fl < flen;){
print FNR, fifo[fl++]} }
##
## Ordinal ranking in file: ranking_o.awk
##
function o_rank(){ print FNR, $0 }
//{o_rank() }
##
## Standard competition ranking in file: ranking_sc.awk
##
BEGIN{ lastresult = lastrank = "!" }
function sc_rank(){
if($1==lastresult){
print lastrank, $0
}else{
print FNR, $0
lastresult = $1
lastrank = FNR}
}
//{sc_rank()}
The input as a file ranking.txt:
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
{{output}}
C:\Users\RC\Code>awk -f ranking_sc.awk ranking.txt
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
C:\Users\RC\Code>awk -f ranking_mc.awk ranking.txt
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
C:\Users\RC\Code>awk -f ranking_d.awk ranking.txt
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
C:\Users\RC\Code>awk -f ranking_o.awk ranking.txt
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
C:\Users\RC\Code>awk -f ranking_f.awk ranking.txt
1 44 Solomon
2.5 42 Jason
2.5 42 Errol
5 41 Garry
5 41 Bernard
5 41 Barry
7 39 Stephen
C:\Users\RC\Code>
C
Takes the scores as input via a file, prints out usage on incorrect invocation.
#include<stdlib.h> #include<stdio.h> typedef struct{ int score; char name[100]; }entry; void ordinalRanking(entry* list,int len){ int i; printf("\n\nOrdinal Ranking\n---------------"); for(i=0;i<len;i++) printf("\n%d\t%d\t%s",i+1,list[i].score,list[i].name); } void standardRanking(entry* list,int len){ int i,j=1; printf("\n\nStandard Ranking\n----------------"); for(i=0;i<len;i++){ printf("\n%d\t%d\t%s",j,list[i].score,list[i].name); if(list[i+1].score<list[i].score) j = i+2; } } void denseRanking(entry* list,int len){ int i,j=1; printf("\n\nDense Ranking\n-------------"); for(i=0;i<len;i++){ printf("\n%d\t%d\t%s",j,list[i].score,list[i].name); if(list[i+1].score<list[i].score) j++; } } void modifiedRanking(entry* list,int len){ int i,j,count; printf("\n\nModified Ranking\n----------------"); for(i=0;i<len-1;i++){ if(list[i].score!=list[i+1].score){ printf("\n%d\t%d\t%s",i+1,list[i].score,list[i].name); count = 1; for(j=i+1;list[j].score==list[j+1].score && j<len-1;j++) count ++; for(j=0;j<count-1;j++) printf("\n%d\t%d\t%s",i+count+1,list[i+j+1].score,list[i+j+1].name); i += (count-1); } } printf("\n%d\t%d\t%s",len,list[len-1].score,list[len-1].name); } void fractionalRanking(entry* list,int len){ int i,j,count; float sum = 0; printf("\n\nFractional Ranking\n------------------"); for(i=0;i<len;i++){ if(i==len-1 || list[i].score!=list[i+1].score) printf("\n%.1f\t%d\t%s",(float)(i+1),list[i].score,list[i].name); else if(list[i].score==list[i+1].score){ sum = i; count = 1; for(j=i;list[j].score==list[j+1].score;j++){ sum += (j+1); count ++; } for(j=0;j<count;j++) printf("\n%.1f\t%d\t%s",sum/count + 1,list[i+j].score,list[i+j].name); i += (count-1); } } } void processFile(char* fileName){ FILE* fp = fopen(fileName,"r"); entry* list; int i,num; fscanf(fp,"%d",&num); list = (entry*)malloc(num*sizeof(entry)); for(i=0;i<num;i++) fscanf(fp,"%d%s",&list[i].score,list[i].name); fclose(fp); ordinalRanking(list,num); standardRanking(list,num); denseRanking(list,num); modifiedRanking(list,num); fractionalRanking(list,num); } int main(int argC,char* argV[]) { if(argC!=2) printf("Usage %s <score list file>"); else processFile(argV[1]); return 0; }
Input file, first row is number of records :
7
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
Output :
C:\rosettaCode>ranking.exe rankData.txt
Ordinal Ranking
---------------
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Standard Ranking
----------------
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Dense Ranking
-------------
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Modified Ranking
----------------
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Fractional Ranking
------------------
1.0 44 Solomon
2.5 42 Jason
2.5 42 Errol
5.0 41 Garry
5.0 41 Bernard
5.0 41 Barry
7.0 39 Stephen
C++
{{trans|C#}}
#include <algorithm> #include <iomanip> #include <iostream> #include <map> #include <ostream> #include <set> #include <vector> template<typename T> std::ostream& print(std::ostream& os, const T& src) { auto it = src.cbegin(); auto end = src.cend(); os << "["; if (it != end) { os << *it; it = std::next(it); } while (it != end) { os << ", " << *it; it = std::next(it); } return os << "]"; } typedef std::map<std::string, int> Map; typedef Map::value_type MapEntry; void standardRank(const Map& scores) { std::cout << "Standard Rank" << std::endl; std::vector<int> list; for (auto& elem : scores) { list.push_back(elem.second); } std::sort(list.begin(), list.end(), std::greater<int>{}); list.erase(std::unique(list.begin(), list.end()), list.end()); int rank = 1; for (auto value : list) { int temp = rank; for (auto& e : scores) { if (e.second == value) { std::cout << temp << " " << value << " " << e.first.c_str() << std::endl; rank++; } } } std::cout << std::endl; } void modifiedRank(const Map& scores) { std::cout << "Modified Rank" << std::endl; std::vector<int> list; for (auto& elem : scores) { list.push_back(elem.second); } std::sort(list.begin(), list.end(), std::greater<int>{}); list.erase(std::unique(list.begin(), list.end()), list.end()); int rank = 0; for (auto value : list) { rank += std::count_if(scores.begin(), scores.end(), [value](const MapEntry& e) { return e.second == value; }); for (auto& e : scores) { if (e.second == value) { std::cout << rank << " " << value << " " << e.first.c_str() << std::endl; } } } std::cout << std::endl; } void denseRank(const Map& scores) { std::cout << "Dense Rank" << std::endl; std::vector<int> list; for (auto& elem : scores) { list.push_back(elem.second); } std::sort(list.begin(), list.end(), std::greater<int>{}); list.erase(std::unique(list.begin(), list.end()), list.end()); int rank = 1; for (auto value : list) { for (auto& e : scores) { if (e.second == value) { std::cout << rank << " " << value << " " << e.first.c_str() << std::endl; } } rank++; } std::cout << std::endl; } void ordinalRank(const Map& scores) { std::cout << "Ordinal Rank" << std::endl; std::vector<int> list; for (auto& elem : scores) { list.push_back(elem.second); } std::sort(list.begin(), list.end(), std::greater<int>{}); list.erase(std::unique(list.begin(), list.end()), list.end()); int rank = 1; for (auto value : list) { for (auto& e : scores) { if (e.second == value) { std::cout << rank++ << " " << value << " " << e.first.c_str() << std::endl; } } } std::cout << std::endl; } void fractionalRank(const Map& scores) { std::cout << "Ordinal Rank" << std::endl; std::vector<int> list; for (auto& elem : scores) { list.push_back(elem.second); } std::sort(list.begin(), list.end(), std::greater<int>{}); list.erase(std::unique(list.begin(), list.end()), list.end()); int rank = 0; for (auto value : list) { double avg = 0.0; int cnt = 0; for (auto& e : scores) { if (e.second == value) { rank++; cnt++; avg += rank; } } avg /= cnt; for (auto& e : scores) { if (e.second == value) { std::cout << std::setprecision(1) << std::fixed << avg << " " << value << " " << e.first.c_str() << std::endl; } } } std::cout << std::endl; } int main() { using namespace std; map<string, int> scores{ {"Solomon", 44}, {"Jason", 42}, {"Errol", 42}, {"Gary", 41}, {"Bernard", 41}, {"Barry", 41}, {"Stephen", 39} }; standardRank(scores); modifiedRank(scores); denseRank(scores); ordinalRank(scores); fractionalRank(scores); return 0; }
{{out}}
Standard Rank
1 44 Solomon
2 42 Errol
2 42 Jason
4 41 Barry
4 41 Bernard
4 41 Gary
7 39 Stephen
Modified Rank
1 44 Solomon
3 42 Errol
3 42 Jason
6 41 Barry
6 41 Bernard
6 41 Gary
7 39 Stephen
Dense Rank
1 44 Solomon
2 42 Errol
2 42 Jason
3 41 Barry
3 41 Bernard
3 41 Gary
4 39 Stephen
Ordinal Rank
1 44 Solomon
2 42 Errol
3 42 Jason
4 41 Barry
5 41 Bernard
6 41 Gary
7 39 Stephen
Ordinal Rank
1.0 44 Solomon
2.5 42 Errol
2.5 42 Jason
5.0 41 Barry
5.0 41 Bernard
5.0 41 Gary
7.0 39 Stephen
C#
{{trans|D}}
using System; using System.Collections.Generic; using System.Linq; namespace RankingMethods { class Program { static void Main(string[] args) { Dictionary<string, int> scores = new Dictionary<string, int> { ["Solomon"] = 44, ["Jason"] = 42, ["Errol"] = 42, ["Gary"] = 41, ["Bernard"] = 41, ["Barry"] = 41, ["Stephen"] = 39, }; StandardRank(scores); ModifiedRank(scores); DenseRank(scores); OrdinalRank(scores); FractionalRank(scores); } static void StandardRank(Dictionary<string, int> data) { Console.WriteLine("Standard Rank"); var list = data.Values.Distinct().ToList(); list.Sort((a, b) => b.CompareTo(a)); int rank = 1; foreach (var value in list) { int temp = rank; foreach (var k in data.Keys) { if (data[k] == value) { Console.WriteLine("{0} {1} {2}", temp, value, k); rank++; } } } Console.WriteLine(); } static void ModifiedRank(Dictionary<string, int> data) { Console.WriteLine("Modified Rank"); var list = data.Values.Distinct().ToList(); list.Sort((a, b) => b.CompareTo(a)); int rank = 0; foreach (var value in list) { foreach (var k in data.Keys) { if (data[k] == value) { rank++; } } foreach (var k in data.Keys) { if (data[k] == value) { Console.WriteLine("{0} {1} {2}", rank, data[k], k); } } } Console.WriteLine(); } static void DenseRank(Dictionary<string, int> data) { Console.WriteLine("Dense Rank"); var list = data.Values.Distinct().ToList(); list.Sort((a, b) => b.CompareTo(a)); int rank = 1; foreach (var value in list) { foreach (var k in data.Keys) { if (data[k] == value) { Console.WriteLine("{0} {1} {2}", rank, data[k], k); } } rank++; } Console.WriteLine(); } static void OrdinalRank(Dictionary<string, int> data) { Console.WriteLine("Ordinal Rank"); var list = data.Values.Distinct().ToList(); list.Sort((a, b) => b.CompareTo(a)); int rank = 1; foreach (var value in list) { foreach (var k in data.Keys) { if (data[k] == value) { Console.WriteLine("{0} {1} {2}", rank, data[k], k); rank++; } } } Console.WriteLine(); } static void FractionalRank(Dictionary<string, int> data) { Console.WriteLine("Fractional Rank"); var list = data.Values.Distinct().ToList(); list.Sort((a, b) => b.CompareTo(a)); int rank = 0; foreach (var value in list) { double avg = 0; int cnt = 0; foreach (var k in data.Keys) { if (data[k] == value) { rank++; cnt++; avg += rank; } } avg /= cnt; foreach (var k in data.Keys) { if (data[k] == value) { Console.WriteLine("{0:F1} {1} {2}", avg, data[k], k); } } } Console.WriteLine(); } } }
{{out}}
Standard Rank
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Gary
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified Rank
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Gary
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense Rank
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Gary
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal Rank
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Gary
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional Rank
1.0 44 Solomon
2.5 42 Jason
2.5 42 Errol
5.0 41 Gary
5.0 41 Bernard
5.0 41 Barry
7.0 39 Stephen
D
import std.algorithm; import std.stdio; void main() { immutable scores = [ "Solomon": 44, "Jason": 42, "Errol": 42, "Garry": 41, "Bernard": 41, "Barry": 41, "Stephen": 39 ]; scores.standardRank; scores.modifiedRank; scores.denseRank; scores.ordinalRank; scores.fractionalRank; } /* Standard ranking 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen */ void standardRank(const int[string] data) { writeln("Standard Rank"); int rank = 1; foreach (value; data.values.dup.sort!"a>b".uniq) { int temp = rank; foreach(k,v; data) { if (v==value) { writeln(temp, " ", v, " ", k); rank++; } } } writeln; } /* Modified ranking 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen */ void modifiedRank(const int[string] data) { writeln("Modified Rank"); int rank = 0; foreach (value; data.values.dup.sort!"a>b".uniq) { foreach(k,v; data) { if (v==value) { rank++; } } foreach(k,v; data) { if (v==value) { writeln(rank, " ", v, " ", k); } } } writeln; } /* Dense ranking 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen */ void denseRank(const int[string] data) { writeln("Dense Rank"); int rank = 1; foreach (value; data.values.dup.sort!"a>b".uniq) { foreach(k,v; data) { if (v==value) { writeln(rank, " ", v, " ", k); } } rank++; } writeln; } /* Ordinal ranking 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen */ void ordinalRank(const int[string] data) { writeln("Ordinal Rank"); int rank = 1; foreach (value; data.values.dup.sort!"a>b".uniq) { foreach(k,v; data) { if (v==value) { writeln(rank, " ", v, " ", k); rank++; } } } writeln; } /* Fractional ranking 1,0 44 Solomon 2,5 42 Jason 2,5 42 Errol 5,0 41 Garry 5,0 41 Bernard 5,0 41 Barry 7,0 39 Stephen */ void fractionalRank(const int[string] data) { writeln("Fractional Rank"); int rank = 0; foreach (value; data.values.dup.sort!"a>b".uniq) { real avg = 0; int cnt; foreach(k,v; data) { if (v==value) { rank++; cnt++; avg+=rank; } } avg /= cnt; foreach(k,v; data) { if (v==value) { writef("%0.1f ", avg); writeln(v, " ", k); } } } writeln; }
{{out}}
Standard Rank
1 44 Solomon
2 42 Errol
2 42 Jason
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified Rank
1 44 Solomon
3 42 Errol
3 42 Jason
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense Rank
1 44 Solomon
2 42 Errol
2 42 Jason
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal Rank
1 44 Solomon
2 42 Errol
3 42 Jason
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional Rank
1.0 44 Solomon
2.5 42 Errol
2.5 42 Jason
5.0 41 Garry
5.0 41 Bernard
5.0 41 Barry
7.0 39 Stephen
Elixir
{{trans|Ruby}}
defmodule Ranking do def methods(data) do IO.puts "stand.\tmod.\tdense\tord.\tfract." Enum.group_by(data, fn {score,_name} -> score end) |> Enum.map(fn {score,pairs} -> names = Enum.map(pairs, fn {_,name} -> name end) |> Enum.reverse {score, names} end) |> Enum.sort_by(fn {score,_} -> -score end) |> Enum.with_index |> Enum.reduce({1,0,0}, fn {{score, names}, i}, {s_rnk, m_rnk, o_rnk} -> d_rnk = i + 1 m_rnk = m_rnk + length(names) f_rnk = ((s_rnk + m_rnk) / 2) |> to_string |> String.replace(".0","") o_rnk = Enum.reduce(names, o_rnk, fn name,acc -> IO.puts "#{s_rnk}\t#{m_rnk}\t#{d_rnk}\t#{acc+1}\t#{f_rnk}\t#{score} #{name}" acc + 1 end) {s_rnk+length(names), m_rnk, o_rnk} end) end end ~w"44 Solomon 42 Jason 42 Errol 41 Garry 41 Bernard 41 Barry 39 Stephen" |> Enum.chunk(2) |> Enum.map(fn [score,name] -> {String.to_integer(score),name} end) |> Ranking.methods
{{out}}
stand. mod. dense ord. fract.
1 1 1 1 1 44 Solomon
2 3 2 2 2.5 42 Jason
2 3 2 3 2.5 42 Errol
4 6 3 4 5 41 Garry
4 6 3 5 5 41 Bernard
4 6 3 6 5 41 Barry
7 7 4 7 7 39 Stephen
Factor
{{works with|Factor|0.99 2019-07-10}}
USING: arrays assocs formatting fry generalizations io kernel
math math.ranges math.statistics math.vectors sequences
splitting.monotonic ;
IN: rosetta-code.ranking
CONSTANT: ranks {
{ 44 "Solomon" } { 42 "Jason" } { 42 "Errol" }
{ 41 "Garry" } { 41 "Bernard" } { 41 "Barry" }
{ 39 "Stephen" }
}
: rank ( seq quot -- seq' )
'[ [ = ] monotonic-split [ length ] map dup @ [ <array> ]
2map concat ] call ; inline
: standard ( seq -- seq' ) [ cum-sum0 1 v+n ] rank ;
: modified ( seq -- seq' ) [ cum-sum ] rank ;
: dense ( seq -- seq' ) [ length [1,b] ] rank ;
: ordinal ( seq -- seq' ) length [1,b] ;
: fractional ( seq -- seq' )
[ dup cum-sum swap [ dupd - [a,b) mean ] 2map ] rank ;
: .rank ( quot -- )
[ ranks dup keys ] dip call swap
[ first2 "%5u %d %s\n" printf ] 2each ; inline
: ranking-demo ( -- )
"Standard ranking" [ standard ]
"Modified ranking" [ modified ]
"Dense ranking" [ dense ]
"Ordinal ranking" [ ordinal ]
"Fractional ranking" [ fractional ]
[ [ print ] [ .rank nl ] bi* ] 2 5 mnapply ;
MAIN: ranking-demo
{{out}}
Standard ranking
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified ranking
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense ranking
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal ranking
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional ranking
1 44 Solomon
2+1/2 42 Jason
2+1/2 42 Errol
5 41 Garry
5 41 Bernard
5 41 Barry
7 39 Stephen
Go
package main import ( "fmt" "sort" ) type rankable interface { Len() int RankEqual(int, int) bool } func StandardRank(d rankable) []float64 { r := make([]float64, d.Len()) var k int for i := range r { if i == 0 || !d.RankEqual(i, i-1) { k = i + 1 } r[i] = float64(k) } return r } func ModifiedRank(d rankable) []float64 { r := make([]float64, d.Len()) for i := range r { k := i + 1 for j := i + 1; j < len(r) && d.RankEqual(i, j); j++ { k = j + 1 } r[i] = float64(k) } return r } func DenseRank(d rankable) []float64 { r := make([]float64, d.Len()) var k int for i := range r { if i == 0 || !d.RankEqual(i, i-1) { k++ } r[i] = float64(k) } return r } func OrdinalRank(d rankable) []float64 { r := make([]float64, d.Len()) for i := range r { r[i] = float64(i + 1) } return r } func FractionalRank(d rankable) []float64 { r := make([]float64, d.Len()) for i := 0; i < len(r); { var j int f := float64(i + 1) for j = i + 1; j < len(r) && d.RankEqual(i, j); j++ { f += float64(j + 1) } f /= float64(j - i) for ; i < j; i++ { r[i] = f } } return r } type scores []struct { score int name string } func (s scores) Len() int { return len(s) } func (s scores) RankEqual(i, j int) bool { return s[i].score == s[j].score } func (s scores) Swap(i, j int) { s[i], s[j] = s[j], s[i] } func (s scores) Less(i, j int) bool { if s[i].score != s[j].score { return s[i].score > s[j].score } return s[i].name < s[j].name } var data = scores{ {44, "Solomon"}, {42, "Jason"}, {42, "Errol"}, {41, "Garry"}, {41, "Bernard"}, {41, "Barry"}, {39, "Stephen"}, } func main() { show := func(name string, fn func(rankable) []float64) { fmt.Println(name, "Ranking:") r := fn(data) for i, d := range data { fmt.Printf("%4v - %2d %s\n", r[i], d.score, d.name) } } sort.Sort(data) show("Standard", StandardRank) show("\nModified", ModifiedRank) show("\nDense", DenseRank) show("\nOrdinal", OrdinalRank) show("\nFractional", FractionalRank) }
{{out}}
Standard Ranking:
1 - 44 Solomon
2 - 42 Errol
2 - 42 Jason
4 - 41 Barry
4 - 41 Bernard
4 - 41 Garry
7 - 39 Stephen
Modified Ranking:
1 - 44 Solomon
3 - 42 Errol
3 - 42 Jason
6 - 41 Barry
6 - 41 Bernard
6 - 41 Garry
7 - 39 Stephen
Dense Ranking:
1 - 44 Solomon
2 - 42 Errol
2 - 42 Jason
3 - 41 Barry
3 - 41 Bernard
3 - 41 Garry
4 - 39 Stephen
Ordinal Ranking:
1 - 44 Solomon
2 - 42 Errol
3 - 42 Jason
4 - 41 Barry
5 - 41 Bernard
6 - 41 Garry
7 - 39 Stephen
Fractional Ranking:
1 - 44 Solomon
2.5 - 42 Errol
2.5 - 42 Jason
5 - 41 Barry
5 - 41 Bernard
5 - 41 Garry
7 - 39 Stephen
Haskell
import Data.List (groupBy, sortBy, intercalate) type Item = (Int, String) type ItemList = [Item] type ItemGroups = [ItemList] type RankItem a = (a, Int, String) type RankItemList a = [RankItem a] -- make sure the input is ordered and grouped by score prepare :: ItemList -> ItemGroups prepare = groupBy gf . sortBy (flip compare) where gf (a, _) (b, _) = a == b -- give an item a rank rank :: Num a => a -> Item -> RankItem a rank n (a, b) = (n, a, b) -- ranking methods standard, modified, dense, ordinal :: ItemGroups -> RankItemList Int standard = ms 1 where ms _ [] = [] ms n (x:xs) = (rank n <$> x) ++ ms (n + length x) xs modified = md 1 where md _ [] = [] md n (x:xs) = let l = length x nl = n + l nl1 = nl - 1 in (rank nl1 <$> x) ++ md (n + l) xs dense = md 1 where md _ [] = [] md n (x:xs) = map (rank n) x ++ md (n + 1) xs ordinal = zipWith rank [1 ..] . concat fractional :: ItemGroups -> RankItemList Double fractional = mf 1.0 where mf _ [] = [] mf n (x:xs) = let l = length x o = take l [n ..] ld = fromIntegral l a = sum o / ld in map (rank a) x ++ mf (n + ld) xs -- sample data test :: ItemGroups test = prepare [ (44, "Solomon") , (42, "Jason") , (42, "Errol") , (41, "Garry") , (41, "Bernard") , (41, "Barry") , (39, "Stephen") ] -- print rank items nicely nicePrint :: Show a => String -> RankItemList a -> IO () nicePrint xs items = do putStrLn xs mapM_ np items putStr "\n" where np (a, b, c) = putStrLn $ intercalate "\t" [show a, show b, c] main :: IO () main = do nicePrint "Standard:" $ standard test nicePrint "Modified:" $ modified test nicePrint "Dense:" $ dense test nicePrint "Ordinal:" $ ordinal test nicePrint "Fractional:" $ fractional test
{{Out}}
Standard:
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified:
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense:
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal:
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional:
1.0 44 Solomon
2.5 42 Jason
2.5 42 Errol
5.0 41 Garry
5.0 41 Bernard
5.0 41 Barry
7.0 39 Stephen
J
Implementation:
competitors=:<;._1;._2]0 :0
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
)
scores=: {."1
standard=: 1+i.~
modified=: 1+i:~
dense=: #/.~ # #\@~.
ordinal=: #\
fractional=: #/.~ # ] (+/%#)/. #\
rank=:1 :'<"0@u@:scores,.]'
Note that we assume that the competitors are already in the right order. Also, of course (as is common when using J) we use the J command line, because that is portable across operating systems (for example: the OS command line is difficult to use on phones).
Task examples:
standard rank competitors
┌─┬──┬───────┐
│1│44│Solomon│
├─┼──┼───────┤
│2│42│Jason │
├─┼──┼───────┤
│2│42│Errol │
├─┼──┼───────┤
│4│41│Garry │
├─┼──┼───────┤
│4│41│Bernard│
├─┼──┼───────┤
│4│41│Barry │
├─┼──┼───────┤
│7│39│Stephen│
└─┴──┴───────┘
modified rank competitors
┌─┬──┬───────┐
│1│44│Solomon│
├─┼──┼───────┤
│3│42│Jason │
├─┼──┼───────┤
│3│42│Errol │
├─┼──┼───────┤
│6│41│Garry │
├─┼──┼───────┤
│6│41│Bernard│
├─┼──┼───────┤
│6│41│Barry │
├─┼──┼───────┤
│7│39│Stephen│
└─┴──┴───────┘
dense rank competitors
┌─┬──┬───────┐
│1│44│Solomon│
├─┼──┼───────┤
│2│42│Jason │
├─┼──┼───────┤
│2│42│Errol │
├─┼──┼───────┤
│3│41│Garry │
├─┼──┼───────┤
│3│41│Bernard│
├─┼──┼───────┤
│3│41│Barry │
├─┼──┼───────┤
│4│39│Stephen│
└─┴──┴───────┘
ordinal rank competitors
┌─┬──┬───────┐
│1│44│Solomon│
├─┼──┼───────┤
│2│42│Jason │
├─┼──┼───────┤
│3│42│Errol │
├─┼──┼───────┤
│4│41│Garry │
├─┼──┼───────┤
│5│41│Bernard│
├─┼──┼───────┤
│6│41│Barry │
├─┼──┼───────┤
│7│39│Stephen│
└─┴──┴───────┘
fractional rank competitors
┌───┬──┬───────┐
│1 │44│Solomon│
├───┼──┼───────┤
│2.5│42│Jason │
├───┼──┼───────┤
│2.5│42│Errol │
├───┼──┼───────┤
│5 │41│Garry │
├───┼──┼───────┤
│5 │41│Bernard│
├───┼──┼───────┤
│5 │41│Barry │
├───┼──┼───────┤
│7 │39│Stephen│
└───┴──┴───────┘
Java
{{works with|Java|8}}
import java.util.*; public class RankingMethods { final static String[] input = {"44 Solomon", "42 Jason", "42 Errol", "41 Garry", "41 Bernard", "41 Barry", "39 Stephen"}; public static void main(String[] args) { int len = input.length; Map<String, int[]> map = new TreeMap<>((a, b) -> b.compareTo(a)); for (int i = 0; i < len; i++) { String key = input[i].split("\\s+")[0]; int[] arr; if ((arr = map.get(key)) == null) arr = new int[]{i, 0}; arr[1]++; map.put(key, arr); } int[][] groups = map.values().toArray(new int[map.size()][]); standardRanking(len, groups); modifiedRanking(len, groups); denseRanking(len, groups); ordinalRanking(len); fractionalRanking(len, groups); } private static void standardRanking(int len, int[][] groups) { System.out.println("\nStandard ranking"); for (int i = 0, rank = 0, group = 0; i < len; i++) { if (group < groups.length && i == groups[group][0]) { rank = i + 1; group++; } System.out.printf("%d %s%n", rank, input[i]); } } private static void modifiedRanking(int len, int[][] groups) { System.out.println("\nModified ranking"); for (int i = 0, rank = 0, group = 0; i < len; i++) { if (group < groups.length && i == groups[group][0]) rank += groups[group++][1]; System.out.printf("%d %s%n", rank, input[i]); } } private static void denseRanking(int len, int[][] groups) { System.out.println("\nDense ranking"); for (int i = 0, rank = 0; i < len; i++) { if (rank < groups.length && i == groups[rank][0]) rank++; System.out.printf("%d %s%n", rank, input[i]); } } private static void ordinalRanking(int len) { System.out.println("\nOrdinal ranking"); for (int i = 0; i < len; i++) System.out.printf("%d %s%n", i + 1, input[i]); } private static void fractionalRanking(int len, int[][] groups) { System.out.println("\nFractional ranking"); float rank = 0; for (int i = 0, tmp = 0, group = 0; i < len; i++) { if (group < groups.length && i == groups[group][0]) { tmp += groups[group++][1]; rank = (i + 1 + tmp) / 2.0F; } System.out.printf("%2.1f %s%n", rank, input[i]); } } }
Standard ranking
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified ranking
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense ranking
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal ranking
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional ranking
1,0 44 Solomon
2,5 42 Jason
2,5 42 Errol
5,0 41 Garry
5,0 41 Bernard
5,0 41 Barry
7,0 39 Stephen
JavaScript
ES5
The task formulation doesn't seem to directly explain or determine the order of listing for players whose score is the same.
( This version chooses to use a secondary (alphabetic) sort after the numeric sort by score. That does, of course, affect the ordinal placements for some players)
(function () { var xs = 'Solomon Jason Errol Garry Bernard Barry Stephen'.split(' '), ns = [44, 42, 42, 41, 41, 41, 39], sorted = xs.map(function (x, i) { return { name: x, score: ns[i] }; }).sort(function (a, b) { var c = b.score - a.score; return c ? c : a.name < b.name ? -1 : a.name > b.name ? 1 : 0; }), names = sorted.map(function (x) { return x.name; }), scores = sorted.map(function (x) { return x.score; }), reversed = scores.slice(0).reverse(), unique = scores.filter(function (x, i) { return scores.indexOf(x) === i; }); // RANKINGS AS FUNCTIONS OF SCORES: SORTED, REVERSED AND UNIQUE var rankings = function (score, index) { return { name: names[index], score: score, Ordinal: index + 1, Standard: function (n) { return scores.indexOf(n) + 1; }(score), Modified: function (n) { return reversed.length - reversed.indexOf(n); }(score), Dense: function (n) { return unique.indexOf(n) + 1; }(score), Fractional: function (n) { return ( (scores.indexOf(n) + 1) + (reversed.length - reversed.indexOf(n)) ) / 2; }(score) }; }, tbl = [ 'Name Score Standard Modified Dense Ordinal Fractional'.split(' ') ].concat(scores.map(rankings).reduce(function (a, x) { return a.concat([ [x.name, x.score, x.Standard, x.Modified, x.Dense, x.Ordinal, x.Fractional ] ]); }, [])), //[[a]] -> bool -> s -> s wikiTable = function (lstRows, blnHeaderRow, strStyle) { return '{| class="wikitable" ' + ( strStyle ? 'style="' + strStyle + '"' : '' ) + lstRows.map(function (lstRow, iRow) { var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|'); return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) { return typeof v === 'undefined' ? ' ' : v; }).join(' ' + strDelim + strDelim + ' '); }).join('') + '\n|}'; }; return wikiTable(tbl, true, 'text-align:center'); })();
{{out}}
{| class="wikitable" style="text-align:center" |- ! Name !! Score !! Standard !! Modified !! Dense !! Ordinal !! Fractional |- | Solomon || 44 || 1 || 1 || 1 || 1 || 1 |- | Errol || 42 || 2 || 3 || 2 || 2 || 2.5 |- | Jason || 42 || 2 || 3 || 2 || 3 || 2.5 |- | Barry || 41 || 4 || 6 || 3 || 4 || 5 |- | Bernard || 41 || 4 || 6 || 3 || 5 || 5 |- | Garry || 41 || 4 || 6 || 3 || 6 || 5 |- | Stephen || 39 || 7 || 7 || 4 || 7 || 7 |}
ES6
((() => { const xs = 'Solomon Jason Errol Garry Bernard Barry Stephen'.split(' '), ns = [44, 42, 42, 41, 41, 41, 39]; const sorted = xs.map((x, i) => ({ name: x, score: ns[i] })) .sort((a, b) => { const c = b.score - a.score; return c ? c : a.name < b.name ? -1 : a.name > b.name ? 1 : 0; }); const names = sorted.map(x => x.name), scores = sorted.map(x => x.score), reversed = scores.slice(0) .reverse(), unique = scores.filter((x, i) => scores.indexOf(x) === i); // RANKINGS AS FUNCTIONS OF SCORES: SORTED, REVERSED AND UNIQUE // rankings :: Int -> Int -> Dictonary const rankings = (score, index) => ({ name: names[index], score, Ordinal: index + 1, Standard: scores.indexOf(score) + 1, Modified: reversed.length - reversed.indexOf(score), Dense: unique.indexOf(score) + 1, Fractional: (n => ( (scores.indexOf(n) + 1) + (reversed.length - reversed.indexOf(n)) ) / 2)(score) }); // tbl :: [[[a]]] const tbl = [ 'Name Score Standard Modified Dense Ordinal Fractional'.split(' ') ].concat(scores.map(rankings) .reduce((a, x) => a.concat([ [x.name, x.score, x.Standard, x.Modified, x.Dense, x.Ordinal, x.Fractional ] ]), [])); // wikiTable :: [[[a]]] -> Bool -> String -> String const wikiTable = (lstRows, blnHeaderRow, strStyle) => `{| class="wikitable" ${strStyle ? 'style="' + strStyle + '"' : ''} ${lstRows.map((lstRow, iRow) => { const strDelim = ((blnHeaderRow && !iRow) ? '!' : '|'); return '\n|-\n' + strDelim + ' ' + lstRow .map(v => typeof v === 'undefined' ? ' ' : v) .join(' ' + strDelim + strDelim + ' '); }).join('')}\n|}`; return wikiTable(tbl, true, 'text-align:center'); }))();
{| class="wikitable" style="text-align:center"
|- ! Name !! Score !! Standard !! Modified !! Dense !! Ordinal !! Fractional |- | Solomon || 44 || 1 || 1 || 1 || 1 || 1 |- | Errol || 42 || 2 || 3 || 2 || 2 || 2.5 |- | Jason || 42 || 2 || 3 || 2 || 3 || 2.5 |- | Barry || 41 || 4 || 6 || 3 || 4 || 5 |- | Bernard || 41 || 4 || 6 || 3 || 5 || 5 |- | Garry || 41 || 4 || 6 || 3 || 6 || 5 |- | Stephen || 39 || 7 || 7 || 4 || 7 || 7 |} {{Out}}
jq
We assume the list of players and their scores has already been sorted, and that the list takes the form: [ player1, score1, player2, score2, ...]
For the sake of brevity, only the ranks are printed.
# Ties share what would have been their first ordinal number
def standard_ranking:
. as $raw
| ([range(1;length;2) | $raw[.]]) as $scores
| reduce range(1; $scores|length) as $i
([1]; if $scores[$i - 1] == $scores[$i] then . + [.[-1]]
else . + [$i + 1]
end) ;
def modified_ranking:
# The helper function resolves [ranks, tentative]
# by appending the ranks of the ties to "ranks"
def resolve:
(.[1] | length) as $length
| if $length == 0 then .[0]
else .[1][-1] as $max
| .[0] + ( .[1] | map( $max) )
end ;
. as $raw
| ([range(1;length;2) | $raw[.]]) as $scores
| reduce range(1; $scores|length) as $i
# state: [ranks, tentative]
([ [], [1] ];
if $scores[$i - 1] == $scores[$i] then [.[0], .[1] + [ $i + 1 ]]
else [ resolve, [ $i + 1 ] ]
end )
| resolve ;
def dense_ranking: # next available
. as $raw
| ([range(1;length;2) | $raw[.]]) as $scores
| reduce range(1; $scores|length) as $i
([1]; if $scores[$i - 1] == $scores[$i] then . + [.[-1]]
else . + [ .[-1] + 1]
end );
def ordinal_ranking: # unfair to some!
[ range(1; 1 + length/2) ] ;
def fractional_ranking:
# The helper function resolves [ranks, tentative]
# by appending the averages of the tentative ranks to "ranks"
def resolve:
(.[1] | length) as $length
| if $length == 0 then .[0]
else (.[1] | add / $length) as $avg
| .[0] + ( .[1] | map( $avg) )
end ;
. as $raw
| ([range(1;length;2) | $raw[.]]) as $scores
| reduce range(1; $scores|length) as $i
# state: [ranks, tentative]
([ [], [1] ];
if $scores[$i - 1] == $scores[$i] then [.[0], .[1] + [ $i + 1 ]]
else [ resolve, [ $i + 1 ] ]
end )
| resolve ;
Task
def raw:
[
"Solomon", 44,
"Jason" , 42,
"Errol" , 42,
"Garry" , 41,
"Bernard", 41,
"Barry" , 41,
"Stephen", 39
] ;
def task:
"standard: \( raw | standard_ranking)",
"modified: \( raw | modified_ranking)",
"dense: \( raw | dense_ranking)",
"ordinal: \( raw | ordinal_ranking)",
"fractional: \( raw | fractional_ranking)" ;
task
{{Out}} standard: [1,2,2,4,4,4,7] modified: [1,3,3,6,6,6,7] dense: [1,2,2,3,3,3,4] ordinal: [1,2,3,4,5,6,7] fractional: [1,2.5,2.5,5,5,5,7]
Julia
'''ties''', a helper function used by some of the ranking methods. It lists any duplicated scores.
function ties{T<:Real}(a::Array{T,1}) unique(a[2:end][a[2:end] .== a[1:end-1]]) end
ties assumes that the there are at least 2 scores in the list to be checked, and the calling functions are designed to avoid calls to it in this case.
'''Standard Ranking Function'''
function rankstandard{T<:Real}(a::Array{T,1}) r = collect(1:length(a)) 1 < r[end] || return r for i in ties(a) r[a.==i] = r[a.==i][1] end return r end
'''Modified Ranking Function'''
function rankmodified{T<:Real}(a::Array{T,1}) indexin(a, a) end
'''Dense Ranking Function'''
function rankdense{T<:Real}(a::Array{T,1}) indexin(a, unique(a)) end
'''Ordinal Ranking Function'''
function rankordinal{T<:Real}(a::Array{T,1}) collect(1:length(a)) end
For ordinal ranking, there are a variety of ways of handling tied scores. I've taken the easy way out and assumed that the position in the list already reflects any tie-breaking policy. In this case, there is not much that needs to be done.
'''Fractional Ranking Function'''
function rankfractional{T<:Real}(a::Array{T,1}) r = float64(collect(1:length(a))) 1.0 < r[end] || return r for i in ties(a) r[a.==i] = mean(r[a.==i]) end return r end
'''Main'''
scores = [44, 42, 42, 41, 41, 41, 39] names = ["Solomon", "Jason", "Errol", "Garry", "Bernard", "Barry", "Stephen"] srank = rankstandard(scores) mrank = rankmodified(scores) drank = rankdense(scores) orank = rankordinal(scores) frank = rankfractional(scores) println(" Name Score Std Mod Den Ord Frac") for i in 1:length(scores) print(@sprintf(" %-7s", names[i])) print(@sprintf("%5d ", scores[i])) print(@sprintf("%5d", srank[i])) print(@sprintf("%5d", mrank[i])) print(@sprintf("%5d", drank[i])) print(@sprintf("%5d", orank[i])) print(@sprintf("%7.2f", frank[i])) println() end
{{out}}
Name Score Std Mod Den Ord Frac
Solomon 44 1 1 1 1 1.00
Jason 42 2 3 2 2 2.50
Errol 42 2 3 2 3 2.50
Garry 41 4 6 3 4 5.00
Bernard 41 4 6 3 5 5.00
Barry 41 4 6 3 6 5.00
Stephen 39 7 7 4 7 7.00
Kotlin
// version 1.0.6 /* all ranking functions assume the array of Pairs is non-empty and already sorted by decreasing order of scores and then, if the scores are equal, by reverse alphabetic order of names */ fun standardRanking(scores: Array<Pair<Int, String>>): IntArray { val rankings = IntArray(scores.size) rankings[0] = 1 for (i in 1 until scores.size) rankings[i] = if (scores[i].first == scores[i - 1].first) rankings[i - 1] else i + 1 return rankings } fun modifiedRanking(scores: Array<Pair<Int, String>>): IntArray { val rankings = IntArray(scores.size) rankings[0] = 1 for (i in 1 until scores.size) { rankings[i] = i + 1 val currScore = scores[i].first for (j in i - 1 downTo 0) { if (currScore != scores[j].first) break rankings[j] = i + 1 } } return rankings } fun denseRanking(scores: Array<Pair<Int, String>>): IntArray { val rankings = IntArray(scores.size) rankings[0] = 1 var prevRanking = 1 for (i in 1 until scores.size) rankings[i] = if (scores[i].first == scores[i - 1].first) prevRanking else ++prevRanking return rankings } fun ordinalRanking(scores: Array<Pair<Int, String>>) = IntArray(scores.size) { it + 1 } fun fractionalRanking(scores: Array<Pair<Int, String>>): DoubleArray { val rankings = DoubleArray(scores.size) rankings[0] = 1.0 for (i in 1 until scores.size) { var k = i val currScore = scores[i].first for (j in i - 1 downTo 0) { if (currScore != scores[j].first) break k = j } val avg = (k..i).average() + 1.0 for (m in k..i) rankings[m] = avg } return rankings } fun printRankings(title: String, rankings: IntArray, scores: Array<Pair<Int, String>>) { println(title + ":") for (i in 0 until rankings.size) { print ("${rankings[i]} ") println(scores[i].toString().removeSurrounding("(", ")").replace(",", "")) } println() } fun printFractionalRankings(title: String, rankings: DoubleArray, scores: Array<Pair<Int, String>>) { println(title + ":") for (i in 0 until rankings.size) { print ("${"%3.2f".format(rankings[i])} ") println(scores[i].toString().removeSurrounding("(", ")").replace(",", "")) } println() } fun main(args: Array<String>) { val scores = arrayOf(44 to "Solomon", 42 to "Jason", 42 to "Errol", 41 to "Garry", 41 to "Bernard", 41 to "Barry", 39 to "Stephen") printRankings("Standard ranking", standardRanking(scores), scores) printRankings("Modified ranking", modifiedRanking(scores), scores) printRankings("Dense ranking", denseRanking(scores), scores) printRankings("Ordinal ranking", ordinalRanking(scores), scores) printFractionalRankings("Fractional ranking", fractionalRanking(scores), scores) }
{{out}}
Standard ranking:
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Modified ranking:
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Dense ranking:
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Ordinal ranking:
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Fractional ranking:
1.00 44 Solomon
2.50 42 Jason
2.50 42 Errol
5.00 41 Garry
5.00 41 Bernard
5.00 41 Barry
7.00 39 Stephen
Mathematica
data = Transpose@{{44, 42, 42, 41, 41, 41, 39}, {"Solomon", "Jason",
"Errol", "Garry", "Bernard", "Barry", "Stephen"}};
rank[data_, type_] :=
Module[{t = Transpose@{Sort@data, Range[Length@data, 1, -1]}},
Switch[type,
"standard", data/.Rule@@@First/@SplitBy[t, First],
"modified", data/.Rule@@@Last/@SplitBy[t, First],
"dense", data/.Thread[#->Range[Length@#]]&@SplitBy[t, First][[All, 1, 1]],
"ordinal", Reverse@Ordering[data],
"fractional", data/.Rule@@@(Mean[#]/.{a_Rational:>N[a]}&)/@ SplitBy[t, First]]]
fmtRankedData[data_, type_] :=
Labeled[Grid[
SortBy[ArrayFlatten@{{Transpose@{rank[data[[All, 1]], type]},
data}}, First], Alignment->Left], type<>" ranking:", Top]
Grid@{fmtRankedData[data, #] & /@ {"standard", "modified", "dense",
"ordinal", "fractional"}}
{{out}}
standard ranking:
1 44 Solomon
3 42 Errol
3 42 Jason
6 41 Barry
6 41 Bernard
6 41 Garry
7 39 Stephen
modified ranking:
1 44 Solomon
2 42 Errol
2 42 Jason
4 41 Barry
4 41 Bernard
4 41 Garry
7 39 Stephen
dense ranking:
1 39 Stephen
2 41 Barry
2 41 Bernard
2 41 Garry
3 42 Errol
3 42 Jason
4 44 Solomon
ordinal ranking:
1 44 Solomon
2 42 Errol
3 42 Jason
4 41 Barry
5 41 Bernard
6 41 Garry
7 39 Stephen
fractional ranking:
1 44 Solomon
2.5 42 Errol
2.5 42 Jason
5 41 Barry
5 41 Bernard
5 41 Garry
7 39 Stephen
=={{header|Modula-2}}== {{trans|C}}
MODULE RankingMethods;
FROM FormatString IMPORT FormatString;
FROM RealStr IMPORT RealToFixed;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteCard(c : CARDINAL);
VAR buf : ARRAY[0..15] OF CHAR;
BEGIN
FormatString("%c", buf, c);
WriteString(buf)
END WriteCard;
TYPE Entry = RECORD
name : ARRAY[0..15] OF CHAR;
score : CARDINAL;
END;
PROCEDURE OrdinalRanking(CONST entries : ARRAY OF Entry);
VAR
buf : ARRAY[0..31] OF CHAR;
i : CARDINAL;
BEGIN
WriteString("Ordinal Ranking");
WriteLn;
WriteString("---------------");
WriteLn;
FOR i:=0 TO HIGH(entries) DO
FormatString("%c\t%c\t%s\n", buf, i + 1, entries[i].score, entries[i].name);
WriteString(buf)
END;
WriteLn
END OrdinalRanking;
PROCEDURE StandardRanking(CONST entries : ARRAY OF Entry);
VAR
buf : ARRAY[0..31] OF CHAR;
i,j : CARDINAL;
BEGIN
WriteString("Standard Ranking");
WriteLn;
WriteString("---------------");
WriteLn;
j := 1;
FOR i:=0 TO HIGH(entries) DO
FormatString("%c\t%c\t%s\n", buf, j, entries[i].score, entries[i].name);
WriteString(buf);
IF entries[i+1].score < entries[i].score THEN
j := i + 2
END
END;
WriteLn
END StandardRanking;
PROCEDURE DenseRanking(CONST entries : ARRAY OF Entry);
VAR
buf : ARRAY[0..31] OF CHAR;
i,j : CARDINAL;
BEGIN
WriteString("Dense Ranking");
WriteLn;
WriteString("---------------");
WriteLn;
j := 1;
FOR i:=0 TO HIGH(entries) DO
FormatString("%c\t%c\t%s\n", buf, j, entries[i].score, entries[i].name);
WriteString(buf);
IF entries[i+1].score < entries[i].score THEN
INC(j)
END
END;
WriteLn
END DenseRanking;
PROCEDURE ModifiedRanking(CONST entries : ARRAY OF Entry);
VAR
buf : ARRAY[0..31] OF CHAR;
i,j,count : CARDINAL;
BEGIN
WriteString("Modified Ranking");
WriteLn;
WriteString("---------------");
WriteLn;
i := 0;
j := 1;
WHILE i < HIGH(entries) DO
IF entries[i].score # entries[i+1].score THEN
FormatString("%c\t%c\t%s\n", buf, i+1, entries[i].score, entries[i].name);
WriteString(buf);
count := 1;
FOR j:=i+1 TO HIGH(entries)-1 DO
IF entries[j].score # entries[j+1].score THEN
BREAK
END;
INC(count)
END;
j := 0;
WHILE j < count-1 DO
FormatString("%c\t%c\t%s\n", buf, i+count+1, entries[i+j+1].score, entries[i+j+1].name);
WriteString(buf);
INC(j)
END;
i := i + count - 1
END;
INC(i)
END;
FormatString("%c\t%c\t%s\n\n", buf, HIGH(entries)+1, entries[HIGH(entries)].score, entries[HIGH(entries)].name);
WriteString(buf)
END ModifiedRanking;
PROCEDURE FractionalRanking(CONST entries : ARRAY OF Entry);
VAR
buf : ARRAY[0..32] OF CHAR;
i,j,count : CARDINAL;
sum : REAL;
BEGIN
WriteString("Fractional Ranking");
WriteLn;
WriteString("---------------");
WriteLn;
sum := 0.0;
i := 0;
WHILE i <= HIGH(entries) DO
IF (i = HIGH(entries) - 1) OR (entries[i].score # entries[i+1].score) THEN
RealToFixed(FLOAT(i+1),1,buf);
WriteString(buf);
FormatString("\t%c\t%s\n", buf, entries[i].score, entries[i].name);
WriteString(buf)
ELSE
sum := FLOAT(i);
count := 1;
j := i;
WHILE entries[j].score = entries[j+1].score DO
sum := sum + FLOAT(j + 1);
INC(count);
INC(j)
END;
FOR j:=0 TO count-1 DO
RealToFixed(sum/FLOAT(count)+1.0,1,buf);
WriteString(buf);
FormatString("\t%c\t%s\n", buf, entries[i+j].score, entries[i+j].name);
WriteString(buf)
END;
i := i + count - 1
END;
INC(i)
END
END FractionalRanking;
(* Main *)
TYPE EA = ARRAY[0..6] OF Entry;
VAR entries : EA;
BEGIN
entries := EA{
{"Solomon", 44},
{"Jason", 42},
{"Errol", 42},
{"Garry", 41},
{"Bernard", 41},
{"Barry", 41},
{"Stephen", 39}
};
OrdinalRanking(entries);
StandardRanking(entries);
DenseRanking(entries);
ModifiedRanking(entries);
FractionalRanking(entries);
ReadChar
END RankingMethods.
{{out}}
Ordinal Ranking
---------------
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Standard Ranking
---------------
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
5 41 Barry
7 39 Stephen
Dense Ranking
---------------
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Modified Ranking
---------------
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Fractional Ranking
---------------
1.0 44 Solomon
2.5 42 Jason
2.5 42 Errol
5.0 41 Garry
5.0 41 Bernard
5.0 41 Barry
7.0 39 Stephen
PARI/GP
Replace "2" with "2.0" in fractional if you prefer decimal to fractional.
standard(v)=v=vecsort(v,1,4); my(last=v[1][1]+1); for(i=1,#v, v[i][1]=if(v[i][1]<last,last=v[i][1]; i, v[i-1][1])); v;
modified(v)=v=vecsort(v,1,4); my(last=v[#v][1]-1); forstep(i=#v,1,-1, v[i][1]=if(v[i][1]>last,last=v[i][1]; i, v[i+1][1])); v;
dense(v)=v=vecsort(v,1,4); my(last=v[1][1]+1,rank); for(i=1,#v, v[i][1]=if(v[i][1]<last,last=v[i][1]; rank++, rank)); v;
ordinal(v)=v=vecsort(v,1,4); for(i=1,#v,v[i][1]=i); v;
fractional(v)=my(a=standard(v),b=modified(v)); vector(#v,i,[(a[i][1]+b[i][1])/2,v[i][2]]);
v=[[44,"Solomon"], [42,"Jason"], [42,"Errol"], [41,"Garry"], [41,"Bernard"], [41,"Barry"], [39,"Stephen"]];
standard(v)
modified(v)
dense(v)
ordinal(v)
fractional(v)
{{out}}
%1 = [[1, "Solomon"], [2, "Errol"], [2, "Jason"], [4, "Barry"], [4, "Bernard"], [4, "Garry"], [7, "Stephen"]]
%2 = [[1, "Solomon"], [3, "Errol"], [3, "Jason"], [6, "Barry"], [6, "Bernard"], [6, "Garry"], [7, "Stephen"]]
%3 = [[1, "Solomon"], [2, "Errol"], [2, "Jason"], [3, "Barry"], [3, "Bernard"], [3, "Garry"], [4, "Stephen"]]
%4 = [[1, "Solomon"], [2, "Errol"], [3, "Jason"], [4, "Barry"], [5, "Bernard"], [6, "Garry"], [7, "Stephen"]]
%5 = [[1, "Solomon"], [5/2, "Jason"], [5/2, "Errol"], [5, "Garry"], [5, "Bernard"], [5, "Barry"], [7, "Stephen"]]
Perl
{{trans|Perl 6}}
my %scores = ( 'Solomon' => 44, 'Jason' => 42, 'Errol' => 42, 'Garry' => 41, 'Bernard' => 41, 'Barry' => 41, 'Stephen' => 39 ); sub tiers { my(%s) = @_; my(%h); push @{$h{$s{$_}}}, $_ for keys %s; @{\%h}{reverse sort keys %h}; } sub standard { my(%s) = @_; my($result); my $rank = 1; for my $players (tiers %s) { $result .= "$rank " . join(', ', sort @$players) . "\n"; $rank += @$players; } return $result; } sub modified { my(%s) = @_; my($result); my $rank = 0; for my $players (tiers %s) { $rank += @$players; $result .= "$rank " . join(', ', sort @$players) . "\n"; } return $result; } sub dense { my(%s) = @_; my($n,$result); $result .= sprintf "%d %s\n", ++$n, join(', ', sort @$_) for tiers %s; return $result; } sub ordinal { my(%s) = @_; my($n,$result); for my $players (tiers %s) { $result .= sprintf "%d %s\n", ++$n, $_ for sort @$players; } return $result; } sub fractional { my(%s) = @_; my($result); my $rank = 1; for my $players (tiers %s) { my $beg = $rank; my $end = $rank += @$players; my $avg = 0; $avg += $_/@$players for $beg .. $end-1; $result .= sprintf "%3.1f %s\n", $avg, join ', ', sort @$players; } return $result; } print "Standard:\n" . standard(%scores) . "\n"; print "Modified:\n" . modified(%scores) . "\n"; print "Dense:\n" . dense(%scores) . "\n"; print "Ordinal:\n" . ordinal(%scores) . "\n"; print "Fractional:\n" . fractional(%scores) . "\n";
{{out}}
Standard:
1 Solomon
2 Errol, Jason
4 Barry, Bernard, Garry
7 Stephen
Modified:
1 Solomon
3 Errol, Jason
6 Barry, Bernard, Garry
7 Stephen
Dense:
1 Solomon
2 Errol, Jason
3 Barry, Bernard, Garry
4 Stephen
Ordinal:
1 Solomon
2 Errol
3 Jason
4 Barry
5 Bernard
6 Garry
7 Stephen
Fractional:
1.0 Solomon
2.5 Errol, Jason
5.0 Barry, Bernard, Garry
7.0 Stephen
```
## Perl 6
```perl6
my @scores =
Solomon => 44,
Jason => 42,
Errol => 42,
Garry => 41,
Bernard => 41,
Barry => 41,
Stephen => 39;
sub tiers (@s) { @s.classify(*.value).pairs.sort.reverse.map: { .value».key } }
sub standard (@s) {
my $rank = 1;
gather for tiers @s -> @players {
take $rank => @players;
$rank += @players;
}
}
sub modified (@s) {
my $rank = 0;
gather for tiers @s -> @players {
$rank += @players;
take $rank => @players;
}
}
sub dense (@s) { tiers(@s).map: { ++$_ => @^players } }
sub ordinal (@s) { @s.map: ++$_ => *.key }
sub fractional (@s) {
my $rank = 1;
gather for tiers @s -> @players {
my $beg = $rank;
my $end = $rank += @players;
take [+]($beg ..^ $end) / @players => @players;
}
}
say "Standard:"; .perl.say for standard @scores;
say "\nModified:"; .perl.say for modified @scores;
say "\nDense:"; .perl.say for dense @scores;
say "\nOrdinal:"; .perl.say for ordinal @scores;
say "\nFractional:"; .perl.say for fractional @scores;
```
{{out}}
```txt
Standard:
1 => ["Solomon"]
2 => ["Jason", "Errol"]
4 => ["Garry", "Bernard", "Barry"]
7 => ["Stephen"]
Modified:
1 => ["Solomon"]
3 => ["Jason", "Errol"]
6 => ["Garry", "Bernard", "Barry"]
7 => ["Stephen"]
Dense:
1 => ["Solomon"]
2 => ["Jason", "Errol"]
3 => ["Garry", "Bernard", "Barry"]
4 => ["Stephen"]
Ordinal:
1 => "Solomon"
2 => "Jason"
3 => "Errol"
4 => "Garry"
5 => "Bernard"
6 => "Barry"
7 => "Stephen"
Fractional:
1.0 => ["Solomon"]
2.5 => ["Jason", "Errol"]
5.0 => ["Garry", "Bernard", "Barry"]
7.0 => ["Stephen"]
```
## Phix
```Phix
function ties(sequence scores)
sequence t = {}, -- {start,num} pairs
tdx = repeat(0,length(scores))
integer last = -1
for i=1 to length(scores) do
integer this = scores[i][1]
if this=last then
t[$][2] += 1
else
t = append(t,{i,1})
end if
tdx[i] = length(t)
last = this
end for
-- eg {{{1,1},{2,2},{4,3},{7,1}},
-- {1,2,2,3,3,3,4}}
return {t,tdx}
end function
enum STANDARD, -- eg {1,2,2,4,4,4,7}
MODIFIED, -- eg {1,3,3,6,6,6,7}
DENSE, -- (==tdx)
ORDINAL, -- eg {1,2,3,4,5,6,7}
FRACTION, -- {1,2.5,2.5,5,5,5,7}
METHODS = $
function rank(integer i, method, sequence t, tdx)
integer idx = tdx[i],
{tx,tn} = t[idx]
switch method
case STANDARD: return tx
case MODIFIED: return tx+tn-1
case DENSE : return idx
case ORDINAL : return i
case FRACTION: return tx+(tn-1)/2
end switch
end function
constant scores = {{44, "Solomon"},
{42, "Jason"},
{42, "Errol"},
{41, "Garry"},
{41, "Bernard"},
{41, "Barry"},
{39, "Stephen"}}
sequence {t,tdx} = ties(scores)
printf(1," score name standard modified dense ordinal fractional\n")
for i=1 to length(scores) do
sequence ranks = repeat(0,METHODS)
for method=1 to METHODS do
ranks[method] = rank(i,method,t,tdx)
end for
printf(1,"%5d %-7s %6g %8g %6g %6g %9g\n",scores[i]&ranks)
end for
```
{{out}}
```txt
score name standard modified dense ordinal fractional
44 Solomon 1 1 1 1 1
42 Jason 2 3 2 2 2.5
42 Errol 2 3 2 3 2.5
41 Garry 4 6 3 4 5
41 Bernard 4 6 3 5 5
41 Barry 4 6 3 6 5
39 Stephen 7 7 4 7 7
```
## PowerShell
```PowerShell
function Get-Ranking
{
[CmdletBinding(DefaultParameterSetName="Standard")]
[OutputType([PSCustomObject])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true,
Position=0)]
[string]
$InputObject,
[Parameter(Mandatory=$false,
ParameterSetName="Standard")]
[switch]
$Standard,
[Parameter(Mandatory=$false,
ParameterSetName="Modified")]
[switch]
$Modified,
[Parameter(Mandatory=$false,
ParameterSetName="Dense")]
[switch]
$Dense,
[Parameter(Mandatory=$false,
ParameterSetName="Ordinal")]
[switch]
$Ordinal,
[Parameter(Mandatory=$false,
ParameterSetName="Fractional")]
[switch]
$Fractional
)
Begin
{
function Get-OrdinalRank ([PSCustomObject[]]$Values)
{
for ($i = 0; $i -lt $Values.Count; $i++)
{
$Values[$i].Rank = $i + 1
}
$Values
}
function Get-Rank ([PSCustomObject[]]$Scores)
{
foreach ($score in $Scores)
{
$score.Group | ForEach-Object {$_.Rank = $score.Rank}
}
$Scores.Group
}
function New-Competitor ([string]$Name, [int]$Score, [int]$Rank = 0)
{
[PSCustomObject]@{
Name = $Name
Score = $Score
Rank = $Rank
}
}
$competitors = @()
$scores = @()
}
Process
{
@($input) | ForEach-Object {$competitors += New-Competitor -Name $_.Split()[1] -Score $_.Split()[0]}
}
End
{
$scores = $competitors |
Sort-Object -Property Score -Descending |
Group-Object -Property Score |
Select-Object -Property @{Name="Score"; Expression={[int]$_.Name}}, @{Name="Rank"; Expression={0}}, Count, Group
switch ($PSCmdlet.ParameterSetName)
{
"Standard"
{
$rank = 1
for ($i = 0; $i -lt $scores.Count; $i++)
{
$scores[$i].Rank = $rank
$rank += $scores[$i].Count
}
Get-Rank $scores
}
"Modified"
{
$rank = 0
foreach ($score in $scores)
{
$rank = $score.Count + $rank
$score.Rank = $rank
}
Get-Rank $scores
}
"Dense"
{
for ($i = 0; $i -lt $scores.Count; $i++)
{
$scores[$i].Rank = $i + 1
}
Get-Rank $scores
}
"Ordinal"
{
Get-OrdinalRank $competitors
}
"Fractional"
{
Get-OrdinalRank $competitors | Group-Object -Property Score | ForEach-Object {
if ($_.Count -gt 1)
{
$rank = ($_.Group.Rank | Measure-Object -Average).Average
foreach ($competitor in $_.Group)
{
$competitor.Rank = $rank
}
}
}
$competitors
}
}
}
}
```
```PowerShell
$scores = "44 Solomon","42 Jason","42 Errol","41 Garry","41 Bernard","41 Barry","39 Stephen"
```
```PowerShell
$scores | Get-Ranking -Standard
```
{{Out}}
```txt
Name Score Rank
---- ----- ----
Solomon 44 1
Jason 42 2
Errol 42 2
Garry 41 4
Bernard 41 4
Barry 41 4
Stephen 39 7
```
```PowerShell
$scores | Get-Ranking -Modified
```
{{Out}}
```txt
Name Score Rank
---- ----- ----
Solomon 44 1
Jason 42 3
Errol 42 3
Garry 41 6
Bernard 41 6
Barry 41 6
Stephen 39 7
```
```PowerShell
$scores | Get-Ranking -Dense
```
{{Out}}
```txt
Name Score Rank
---- ----- ----
Solomon 44 1
Jason 42 2
Errol 42 2
Garry 41 3
Bernard 41 3
Barry 41 3
Stephen 39 4
```
```PowerShell
$scores | Get-Ranking -Ordinal
```
{{Out}}
```txt
Name Score Rank
---- ----- ----
Solomon 44 1
Jason 42 2
Errol 42 3
Garry 41 4
Bernard 41 5
Barry 41 6
Stephen 39 7
```
```PowerShell
$scores | Get-Ranking -Fractional
```
{{Out}}
```txt
Name Score Rank
---- ----- ----
Solomon 44 1
Jason 42 2.5
Errol 42 2.5
Garry 41 5
Bernard 41 5
Barry 41 5
Stephen 39 7
```
## Python
```python
def mc_rank(iterable, start=1):
"""Modified competition ranking"""
lastresult, fifo = None, []
for n, item in enumerate(iterable, start-1):
if item[0] == lastresult:
fifo += [item]
else:
while fifo:
yield n, fifo.pop(0)
lastresult, fifo = item[0], fifo + [item]
while fifo:
yield n+1, fifo.pop(0)
def sc_rank(iterable, start=1):
"""Standard competition ranking"""
lastresult, lastrank = None, None
for n, item in enumerate(iterable, start):
if item[0] == lastresult:
yield lastrank, item
else:
yield n, item
lastresult, lastrank = item[0], n
def d_rank(iterable, start=1):
"""Dense ranking"""
lastresult, lastrank = None, start - 1,
for item in iterable:
if item[0] == lastresult:
yield lastrank, item
else:
lastresult, lastrank = item[0], lastrank + 1
yield lastrank, item
def o_rank(iterable, start=1):
"""Ordinal ranking"""
yield from enumerate(iterable, start)
def f_rank(iterable, start=1):
"""Fractional ranking"""
last, fifo = None, []
for n, item in enumerate(iterable, start):
if item[0] != last:
if fifo:
mean = sum(f[0] for f in fifo) / len(fifo)
while fifo:
yield mean, fifo.pop(0)[1]
last = item[0]
fifo.append((n, item))
if fifo:
mean = sum(f[0] for f in fifo) / len(fifo)
while fifo:
yield mean, fifo.pop(0)[1]
if __name__ == '__main__':
scores = [(44, 'Solomon'),
(42, 'Jason'),
(42, 'Errol'),
(41, 'Garry'),
(41, 'Bernard'),
(41, 'Barry'),
(39, 'Stephen')]
print('\nScores to be ranked (best first):')
for s in scores:
print(' %2i %s' % (s ))
for ranker in [sc_rank, mc_rank, d_rank, o_rank, f_rank]:
print('\n%s:' % ranker.__doc__)
for rank, score in ranker(scores):
print(' %3g, %r' % (rank, score))
```
{{out}}
```txt
Scores to be ranked (best first):
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
Standard competition ranking:
1, (44, 'Solomon')
2, (42, 'Jason')
2, (42, 'Errol')
4, (41, 'Garry')
4, (41, 'Bernard')
4, (41, 'Barry')
7, (39, 'Stephen')
Modified competition ranking:
1, (44, 'Solomon')
3, (42, 'Jason')
3, (42, 'Errol')
6, (41, 'Garry')
6, (41, 'Bernard')
6, (41, 'Barry')
7, (39, 'Stephen')
Dense ranking:
1, (44, 'Solomon')
2, (42, 'Jason')
2, (42, 'Errol')
3, (41, 'Garry')
3, (41, 'Bernard')
3, (41, 'Barry')
4, (39, 'Stephen')
Ordinal ranking:
1, (44, 'Solomon')
2, (42, 'Jason')
3, (42, 'Errol')
4, (41, 'Garry')
5, (41, 'Bernard')
6, (41, 'Barry')
7, (39, 'Stephen')
Fractional ranking:
1, (44, 'Solomon')
2.5, (42, 'Jason')
2.5, (42, 'Errol')
5, (41, 'Garry')
5, (41, 'Bernard')
5, (41, 'Barry')
7, (39, 'Stephen')
```
## Racket
```racket
#lang racket
;; Tim-brown 2014-09-11
;; produces a ranking according to ranking function: rfn
;; INPUT:
;; lst : (list (score . details))
;; rfn : (length-scores)
;; -> (values
;; ranks-added ; how many ranks to add for the next iteration
;; (idx . rest -> rank-offset)) ; function that produces the rank for the idx^th element
;; ; in the scoring (arity must be >= 1)
(define (rank-list all-scores rfn)
(let loop ((rank-0 0) (lst (sort all-scores > #:key car)) (acc empty))
(cond
[(null? lst) acc]
[else
(define 1st-score (caar lst))
(define (ties-with-1st? cand) (= (car cand) 1st-score))
(define-values (tied unranked) (splitf-at lst ties-with-1st?))
;; all ranking functions should properly handle a singleton tied list
(define tied-len (length tied))
(define tied? (> tied-len 1))
(define-values (ranks-added rank-offset-fn) (rfn tied-len))
(define ranked-tied (for/list ((t (in-list tied)) (i (in-naturals 1)))
(list* tied? (+ rank-0 (rank-offset-fn i)) t)))
(loop (+ ranks-added rank-0) unranked (append acc ranked-tied))])))
;; Ties share what would have been their first ordinal number
(define (rank-function:Standard l)
(values l (thunk* 1)))
;; Ties share what would have been their last ordinal number
(define (rank-function:Modified l)
(values l (thunk* l)))
;; Ties share the next available integer
(define (rank-function:Dense l)
(values 1 (thunk* 1)))
;; Competitors take the next available integer. Ties are not treated otherwise
(define (rank-function:Ordinal l)
(values l (λ (n . _) n)))
;; Ties share the mean of what would have been their ordinal numbers
(define (rank-function:Fractional l)
(values l (thunk* (/ (+ l 1) 2))))
(define score-board
'((44 . Solomon)
(42 . Jason)
(42 . Errol)
(41 . Garry)
(41 . Bernard)
(41 . Barry)
(39 . Stephen)))
(define format-number
(match-lambda
[(? integer? i) i]
[(and f (app numerator n) (app denominator d))
(define-values (q r) (quotient/remainder n d))
(format "~a ~a/~a" q r d)]))
(for ((fn (list
rank-function:Standard
rank-function:Modified
rank-function:Dense
rank-function:Ordinal
rank-function:Fractional)))
(printf "Function: ~s~%" fn)
(for ((r (in-list (rank-list score-board fn))))
(printf "~a ~a\t~a\t~a~%"
(if (car r) "=" " ")
(format-number (cadr r))
(caddr r)
(cdddr r)))
(newline))
```
{{out}}
```txt
Function: #
1 44 Solomon
= 2 42 Jason
= 2 42 Errol
= 4 41 Garry
= 4 41 Bernard
= 4 41 Barry
7 39 Stephen
Function: #
1 44 Solomon
= 3 42 Jason
= 3 42 Errol
= 6 41 Garry
= 6 41 Bernard
= 6 41 Barry
7 39 Stephen
Function: #
1 44 Solomon
= 2 42 Jason
= 2 42 Errol
= 3 41 Garry
= 3 41 Bernard
= 3 41 Barry
4 39 Stephen
Function: #
1 44 Solomon
= 2 42 Jason
= 3 42 Errol
= 4 41 Garry
= 5 41 Bernard
= 6 41 Barry
7 39 Stephen
Function: #
1 44 Solomon
= 2 1/2 42 Jason
= 2 1/2 42 Errol
= 5 41 Garry
= 5 41 Bernard
= 5 41 Barry
7 39 Stephen
```
## REXX
```rexx
/**************************
44 Solomon 1 1 1 1 1
42 Jason 2 3 2 2 2.5
42 Errol 2 3 2 3 2.5
41 Garry 4 6 3 4 5
41 Bernard 4 6 3 5 5
41 Barry 4 6 3 6 5
39 Stephen 7 7 4 7 7
**************************/
Do i=1 To 7
Parse Value sourceline(i+1) With rank.i name.i .
/* say rank.i name.i */
End
pool=0
crank=0
Do i=1 To 7
If rank.i<>crank Then Do
pool=pool+1
lo.pool=i
hi.pool=i
n.pool=1
ii.pool=i
End
Else Do
n.pool=n.pool+1
hi.pool=i
ii.pool=ii.pool+i
End
crank=rank.i
pool.i=pool
End
/*
Do j=1 To pool
Say 'pool' j n.j lo.j hi.j
End
*/
cp=0
r=0
cnt.=0
Do i=1 To 7
p=pool.i
If p<>cp Then
r=r+1
res=rank.i left(name.i,8) lo.p hi.p r i ii.p/n.p
If res=sourceline(i+1) Then cnt.ok=cnt.ok+1
Say res
cp=p
End
Say cnt.ok 'correct lines'
```
{{out}}
```txt
44 Solomon 1 1 1 1 1
42 Jason 2 3 2 2 2.5
42 Errol 2 3 2 3 2.5
41 Garry 4 6 3 4 5
41 Bernard 4 6 3 5 5
41 Barry 4 6 3 6 5
39 Stephen 7 7 4 7 7
7 correct lines
```
## Ruby
```ruby
ar = "44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen".lines.map{|line| line.split}
grouped = ar.group_by{|pair| pair.shift.to_i}
s_rnk = 1
m_rnk = o_rnk = 0
puts "stand.\tmod.\tdense\tord.\tfract."
grouped.each.with_index(1) do |(score, names), d_rnk|
m_rnk += names.flatten!.size
f_rnk = (s_rnk + m_rnk)/2.0
names.each do |name|
o_rnk += 1
puts "#{s_rnk}\t#{m_rnk}\t#{d_rnk}\t#{o_rnk}\t#{f_rnk.to_s.sub(".0","")}\t#{score} #{name}"
end
s_rnk += names.size
end
```
{{out}}
```txt
stand. mod. dense ord. fract.
1 1 1 1 1 44 Solomon
2 3 2 2 2.5 42 Jason
2 3 2 3 2.5 42 Errol
4 6 3 4 5 41 Garry
4 6 3 5 5 41 Bernard
4 6 3 6 5 41 Barry
7 7 4 7 7 39 Stephen
```
## Scala
This example uses a type-safe singly-linked object model with no mutable state variables, which makes it longer than the Ruby version above, but demonstrates an object-oriented functional programming approach.
```Scala
object RankingMethods extends App {
case class Score(score: Int, name: String) // incoming data
case class Rank[Precision](rank: Precision, names: List[String]) // outgoing results (can be int or double)
case class State[Precision](n: Int, done: List[Rank[Precision]]) { // internal state, no mutable variables
def next(n: Int, next: Rank[Precision]) = State(n, next :: done)
}
def grouped[Precision](list: List[Score]) = // group names together by score, with highest first
(scala.collection.immutable.TreeMap[Int, List[Score]]() ++ list.groupBy(-_.score))
.values.map(_.map(_.name)).foldLeft(State[Precision](1, Nil)) _
// Ranking methods:
def rankStandard(list: List[Score]) =
grouped[Int](list){case (state, names) => state.next(state.n+names.length, Rank(state.n, names))}.done.reverse
def rankModified(list: List[Score]) =
rankStandard(list).map(r => Rank(r.rank+r.names.length-1, r.names))
def rankDense(list: List[Score]) =
grouped[Int](list){case (state, names) => state.next(state.n+1, Rank(state.n, names))}.done.reverse
def rankOrdinal(list: List[Score]) =
list.zipWithIndex.map{case (score, n) => Rank(n+1, List(score.name))}
def rankFractional(list: List[Score]) =
rankStandard(list).map(r => Rank((2*r.rank+r.names.length-1.0)/2, r.names))
// Tests:
def parseScores(s: String) = s split "\\s+" match {case Array(s,n) => Score(s.toInt, n)}
val test = List("44 Solomon", "42 Jason", "42 Errol", "41 Garry", "41 Bernard", "41 Barry", "39 Stephen").map(parseScores)
println("Standard:")
println(rankStandard(test) mkString "\n")
println("\nModified:")
println(rankModified(test) mkString "\n")
println("\nDense:")
println(rankDense(test) mkString "\n")
println("\nOrdinal:")
println(rankOrdinal(test) mkString "\n")
println("\nFractional:")
println(rankFractional(test) mkString "\n")
}
```
{{out}}
```txt
Standard:
Rank(1,List(Solomon))
Rank(2,List(Jason, Errol))
Rank(4,List(Garry, Bernard, Barry))
Rank(7,List(Stephen))
Modified:
Rank(1,List(Solomon))
Rank(3,List(Jason, Errol))
Rank(6,List(Garry, Bernard, Barry))
Rank(7,List(Stephen))
Dense:
Rank(1,List(Solomon))
Rank(2,List(Jason, Errol))
Rank(3,List(Garry, Bernard, Barry))
Rank(4,List(Stephen))
Ordinal:
Rank(1,List(Solomon))
Rank(2,List(Jason))
Rank(3,List(Errol))
Rank(4,List(Garry))
Rank(5,List(Bernard))
Rank(6,List(Barry))
Rank(7,List(Stephen))
Fractional:
Rank(1.0,List(Solomon))
Rank(2.5,List(Jason, Errol))
Rank(5.0,List(Garry, Bernard, Barry))
Rank(7.0,List(Stephen))
```
## Sidef
{{trans|Perl 6}}
```ruby
var scores = [
Pair(Solomon => 44),
Pair(Jason => 42),
Pair(Errol => 42),
Pair(Garry => 41),
Pair(Bernard => 41),
Pair(Barry => 41),
Pair(Stephen => 39),
]
func tiers(s) {
s.group_by { .value }.kv.sort.flip.map { .value.map{.key} }
}
func standard(s) {
var rank = 1
gather {
for players in tiers(s) {
take(Pair(rank, players))
rank += players.len
}
}
}
func modified(s) {
var rank = 0
gather {
for players in tiers(s) {
rank += players.len
take(Pair(rank, players))
}
}
}
func dense(s) {
tiers(s).map_kv { |k,v| Pair(k+1, v) }
}
func ordinal(s) {
s.map_kv { |k,v| Pair(k+1, v.key) }
}
func fractional(s) {
var rank = 1
gather {
for players in tiers(s) {
var beg = rank
var end = (rank += players.len)
take(Pair(sum(beg ..^ end) / players.len, players))
}
}
}
func display(r) {
say r.map {|a| '%3s : %s' % a... }.join("\n")
}
say "Standard:"; display( standard(scores))
say "\nModified:"; display( modified(scores))
say "\nDense:"; display( dense(scores))
say "\nOrdinal:"; display( ordinal(scores))
say "\nFractional:"; display(fractional(scores))
```
{{out}}
```txt
Standard:
1 : ["Solomon"]
2 : ["Jason", "Errol"]
4 : ["Garry", "Bernard", "Barry"]
7 : ["Stephen"]
Modified:
1 : ["Solomon"]
3 : ["Jason", "Errol"]
6 : ["Garry", "Bernard", "Barry"]
7 : ["Stephen"]
Dense:
1 : ["Solomon"]
2 : ["Jason", "Errol"]
3 : ["Garry", "Bernard", "Barry"]
4 : ["Stephen"]
Ordinal:
1 : Solomon
2 : Jason
3 : Errol
4 : Garry
5 : Bernard
6 : Barry
7 : Stephen
Fractional:
1 : ["Solomon"]
2.5 : ["Jason", "Errol"]
5 : ["Garry", "Bernard", "Barry"]
7 : ["Stephen"]
```
## Tcl
```tcl
proc rank {rankingMethod sortedList} {
# Extract the groups in the data (this is pointless for ordinal...)
set s [set group [set groups {}]]
foreach {score who} $sortedList {
if {$score != $s} {
lappend groups [llength $group]
set s $score
set group {}
}
lappend group $who
}
lappend groups [llength $group]
# Construct the rankings; note that we have a zero-sized leading group
set n 1; set m 0
foreach g $groups {
switch $rankingMethod {
standard {
lappend result {*}[lrepeat $g $n]
incr n $g
}
modified {
lappend result {*}[lrepeat $g [incr m $g]]
}
dense {
lappend result {*}[lrepeat $g $m]
incr m
}
ordinal {
for {set i 0} {$i < $g} {incr i} {
lappend result [incr m]
}
}
fractional {
set val [expr {($n + [incr n $g] - 1) / 2.0}]
lappend result {*}[lrepeat $g [format %g $val]]
}
}
}
return $result
}
set data {
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
39 Stephen
}
foreach method {standard modified dense ordinal fractional} {
puts "Using method '$method'...\n Rank\tScore\tWho"
foreach rank [rank $method $data] {score who} $data {
puts " $rank\t$score\t$who"
}
}
```
{{out}}
```txt
Using method 'standard'...
Rank Score Who
1 44 Solomon
2 42 Jason
2 42 Errol
4 41 Garry
4 41 Bernard
4 41 Barry
7 39 Stephen
Using method 'modified'...
Rank Score Who
1 44 Solomon
3 42 Jason
3 42 Errol
6 41 Garry
6 41 Bernard
6 41 Barry
7 39 Stephen
Using method 'dense'...
Rank Score Who
1 44 Solomon
2 42 Jason
2 42 Errol
3 41 Garry
3 41 Bernard
3 41 Barry
4 39 Stephen
Using method 'ordinal'...
Rank Score Who
1 44 Solomon
2 42 Jason
3 42 Errol
4 41 Garry
5 41 Bernard
6 41 Barry
7 39 Stephen
Using method 'fractional'...
Rank Score Who
1 44 Solomon
2.5 42 Jason
2.5 42 Errol
5 41 Garry
5 41 Bernard
5 41 Barry
7 39 Stephen
```
## Visual FoxPro
```vfp
#DEFINE CTAB CHR(9)
#DEFINE CRLF CHR(13) + CHR(10)
LOCAL lcTxt As String, i As Integer
CLOSE DATABASES ALL
SET SAFETY OFF
CLEAR
CREATE CURSOR scores (score I, name V(8), rownum I AUTOINC)
INDEX ON score TAG score COLLATE "Machine"
SET ORDER TO 0
INSERT INTO scores (score, name) VALUES (44, "Solomon")
INSERT INTO scores (score, name) VALUES (42, "Jason")
INSERT INTO scores (score, name) VALUES (42, "Errol")
INSERT INTO scores (score, name) VALUES (41, "Garry")
INSERT INTO scores (score, name) VALUES (41, "Bernard")
INSERT INTO scores (score, name) VALUES (41, "Barry")
INSERT INTO scores (score, name) VALUES (39, "Stephen")
CREATE CURSOR ranks (sc_rank I, mod_rank I, dense I, ordinal I, fractional B(1), score I, name V(8))
INDEX ON score TAG score COLLATE "Machine"
SET ORDER TO 0
APPEND FROM DBF("scores") FIELDS score, name
Std_Comp()
Modified()
Dense()
Ordinal()
Fractional()
COPY TO ranks.txt TYPE DELIMITED WITH TAB
lcTxt = ""
FOR i = 1 TO FCOUNT()
lcTxt = lcTxt + FIELD(i) + CTAB
ENDFOR
lcTxt = LEFT(lcTxt, LEN(lcTxt) - 1) + CRLF + FILETOSTR("ranks.txt")
STRTOFILE(lcTxt, "ranks.txt")
MODIFY FILE ranks.txt
SET SAFETY ON
FUNCTION ScoreGroup(aa)
LOCAL n As Integer
SELECT score, COUNT(*) As num FROM scores ;
GROUP BY score ORDER BY score DESC INTO ARRAY aa
n = _TALLY
RETURN n
ENDFUNC
PROCEDURE Std_Comp
LOCAL n, i, nn
LOCAL ARRAY a[1]
SELECT ranks
BLANK FIELDS sc_rank ALL
nn = ScoreGroup(@a)
n = 1
FOR i = 1 TO nn
REPLACE sc_rank WITH n FOR score = a[i,1]
n = n + a[i,2]
ENDFOR
ENDPROC
PROCEDURE Modified
LOCAL n, i, nn
LOCAL ARRAY a[1]
SELECT ranks
BLANK FIELDS mod_rank ALL
nn = ScoreGroup(@a)
n = 0
FOR i = 1 TO nn
n = n + a[i,2]
REPLACE mod_rank WITH n FOR score = a[i,1]
ENDFOR
ENDPROC
PROCEDURE Dense
LOCAL n, i, nn
LOCAL ARRAY a[1]
SELECT ranks
BLANK FIELDS dense ALL
nn = ScoreGroup(@a)
SELECT ranks
n = 0
FOR i = 1 TO nn
n = n + a[i,2]
REPLACE dense WITH i FOR score = a[i,1]
ENDFOR
ENDPROC
PROCEDURE Ordinal
SELECT ranks
BLANK FIELDS ordinal ALL
REPLACE ordinal WITH RECNO() ALL
ENDPROC
PROCEDURE Fractional
LOCAL i As Integer, nn As Integer
LOCAL ARRAY a[1]
SELECT ranks
BLANK FIELDS fractional ALL
SELECT CAST(AVG(rownum) As B(1)), score FROM scores ;
GROUP BY score ORDER BY score DESC INTO ARRAY a
nn = _TALLY
FOR i = 1 TO nn
REPLACE fractional WITH a[i,1] FOR score = a[i,2]
ENDFOR
ENDPROC
```
{{out}}
```txt
SC_RANK MOD_RANK DENSE ORDINAL FRACTIONAL SCORE NAME
1 1 1 1 1.0 44 "Solomon"
2 3 2 2 2.5 42 "Jason"
2 3 2 3 2.5 42 "Errol"
4 6 3 4 5.0 41 "Garry"
4 6 3 5 5.0 41 "Bernard"
4 6 3 6 5.0 41 "Barry"
7 7 4 7 7.0 39 "Stephen"
```
## zkl
```zkl
fcn group(scores){ // group like scores into one list --> list of lists
sink:=List();
scores.reduce('wrap(ps,sn,buf){
if(sn[0]!=ps){ sink.append(buf.copy()); buf.clear(); }
buf+sn;
sn[0];
},scores[0][0],buf:=List());
sink.append(buf);
}
fcn print(list,rank){
list.apply2('wrap(sn){ "%2s: %s (%d)".fmt(rank,sn[1],sn[0]):println(_); });
}
fcn rankViaStandard(scores){
rank:=1;
foreach group in (group(scores)){ print(group,rank); rank+=group.len(); }
}
fcn rankViaModified(scores){
rank:=0;
foreach group in (group(scores)){ rank+=group.len(); print(group,rank); }
}
fcn rankViaDense(scores){
rank:=1;
foreach group in (group(scores)){ print(group,rank); rank+=1; }
}
fcn rankViaOrdinal(scores){
scores.apply2('wrap(sn,rr){ "%2s: %s (%d)".fmt(rr.inc(),sn[1],sn[0]):println(_); },Ref(1));
}
fcn rankViaFractional(scores){
rank:=1;
foreach group in (group(scores)){
n:=group.len(); r:=rank.reduce(n,'+,0.0)/n; rank+=n;
print(group,"%5.2f".fmt(r));
}
}
```
```zkl
// these are sorted!?!
scores:=T(T(44,"Solomon"), T(42,"Jason"), T(42,"Errol"), T(41,"Garry"),
T(41,"Bernard"),T(41,"Barry"),T(39,"Stephen"),);
"Standard:" .println(); rankViaStandard(scores);
"Modified:" .println(); rankViaModified(scores);
"Dense:" .println(); rankViaDense(scores);
"Ordinal:" .println(); rankViaOrdinal(scores);
"Fractional:".println(); rankViaFractional(scores);
```
{{out}}
```txt
Standard:
1: Solomon (44)
2: Jason (42)
2: Errol (42)
4: Garry (41)
4: Bernard (41)
4: Barry (41)
7: Stephen (39)
Modified:
1: Solomon (44)
3: Jason (42)
3: Errol (42)
6: Garry (41)
6: Bernard (41)
6: Barry (41)
7: Stephen (39)
Dense:
1: Solomon (44)
2: Jason (42)
2: Errol (42)
3: Garry (41)
3: Bernard (41)
3: Barry (41)
4: Stephen (39)
Ordinal:
1: Solomon (44)
2: Jason (42)
3: Errol (42)
4: Garry (41)
5: Bernard (41)
6: Barry (41)
7: Stephen (39)
Fractional:
1.00: Solomon (44)
2.50: Jason (42)
2.50: Errol (42)
5.00: Garry (41)
5.00: Bernard (41)
5.00: Barry (41)
7.00: Stephen (39)
```