Ranking methods
You are encouraged to solve this task according to the task description, using any language you may know.
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 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 wikipedia article for a fuller description.
Show here, on this page, the ranking of the test scores under each of the numbered ranking methods.
AppleScript
<lang applescript>(*
The five ranking methods are implemented here as script objects sharing inherited code rather than as simple handlers, although there appears to be little advantage either way. This way needs fewer lines of code but more lines of explanatory comments!
- )
use AppleScript version "2.4" -- Mac OS 10.11 (Yosemite) or later (for these 'use' commands). use sorter : script "Custom Iterative Ternary Merge Sort" -- <https://macscripter.net/viewtopic.php?pid=194430#p194430>
script standardRanking
-- Properties and handlers inherited or overridden by the other script objects.
-- The 'references' are to values that won't be available until 'results' is set to a list.
-- 'me' and 'my' refer to the script object using the code at the time.
property results : missing value
property startIndex : 1
property endIndex : a reference to length of (a reference to results)
property step : 1
property currentRank : missing value
property currentScore : missing value
-- Main handler.
on resultsFrom(theScores)
copy theScores to my results
-- The task description specifies that the input list is already ordered, but that's not assumed here.
-- Additionally, competitors with equal scores are arranged alphabetically by name.
-- The comparer here is 'me' because the current script object contains the isGreater(a, b) handler to be used.
tell sorter to sort(my results, my startIndex, my endIndex, {comparer:me})
set my currentScore to score of item (my startIndex) of my results
set my currentRank to my startIndex's contents
repeat with i from (my startIndex) to (my endIndex) by (my step)
my rankResult(i)
end repeat
-- Since these script objects are assigned to top-level variables in a running script, make sure the potentially
-- long 'results' list isn't saved back to the script file with them at the end of the run. This precaution isn't
-- necessary in a library script or if the scripts are instantiated and assigned to local variables at run time.
set localVariable to my results
set my results to missing value
return localVariable
end resultsFrom
-- Comparison handler used by the sort. The returned boolean indicates whether or not record 'a' should go after record 'b'.
on isGreater(a, b)
if (a's score is less than b's score) then return true
return ((a's score is equal to b's score) and (a's competitor comes after b's competitor))
end isGreater
-- Specialist ranking handler. Inherited by the modifiedRanking script, but overridden by the others.
on rankResult(i)
set thisResult to item i of my results
set thisScore to thisResult's score
if (thisScore is not currentScore) then
set my currentRank to i
set my currentScore to thisScore
end if
set item i of my results to thisResult & {rank:my currentRank}
end rankResult
end script
script modifiedRanking -- Uses the standardRanking code, but works backwards through the results list.
property parent : standardRanking property startIndex : a reference to length of (a reference to results) property endIndex : 1 property step : -1
end script
script denseRanking
property parent : standardRanking
on rankResult(i)
set thisResult to item i of my results
set thisScore to thisResult's score
if (thisScore is not my currentScore) then
set my currentRank to (my currentRank) + 1
set my currentScore to thisScore
end if
set item i of my results to thisResult & {rank:my currentRank}
end rankResult
end script
script ordinalRanking
property parent : standardRanking
on rankResult(i)
set item i of my results to (item i of my results) & {rank:i}
end rankResult
end script
script fractionalRanking
property parent : standardRanking
on rankResult(i)
set thisResult to item i of my results
set thisScore to thisResult's score
if (thisScore is not my currentScore) then
-- i and currentRank are simultaneously indices and ranks.
-- The average of any run of consecutive integers is that of the first and last.
set average to (i - 1 + (my currentRank)) / 2
repeat with j from (my currentRank) to (i - 1)
set rank of item j of my results to average
end repeat
set my currentRank to i
set my currentScore to thisScore
end if
set item i of my results to thisResult & {rank:i as real}
end rankResult
end script
-- Task code: on formatRankings(type, theResults)
set rankings to {type}
repeat with thisResult in theResults
set end of rankings to (thisResult's rank as text) & tab & thisResult's competitor & " (" & thisResult's score & ")"
end repeat
return joinStrings(rankings, linefeed)
end formatRankings
on joinStrings(listOfText, delimiter)
set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to delimiter set output to listOfText as text set AppleScript's text item delimiters to astid return output
end joinStrings
local theScores, output set theScores to {{score:44, competitor:"Solomon"}, {score:42, competitor:"Jason"}, {score:42, competitor:"Errol"}, ¬
{score:41, competitor:"Garry"}, {score:41, competitor:"Bernard"}, {score:41, competitor:"Barry"}, ¬
{score:39, competitor:"Stephen"}}
set output to {} set end of output to formatRankings("Standard ranking:", standardRanking's resultsFrom(theScores)) set end of output to formatRankings("Modified ranking:", modifiedRanking's resultsFrom(theScores)) set end of output to formatRankings("Dense ranking:", denseRanking's resultsFrom(theScores)) set end of output to formatRankings("Ordinal ranking:", ordinalRanking's resultsFrom(theScores)) set end of output to formatRankings("Fractional ranking:", fractionalRanking's resultsFrom(theScores)) return joinStrings(output, linefeed & linefeed)</lang>
- Output:
<lang applescript>"Standard ranking: 1 Solomon (44) 2 Errol (42) 2 Jason (42) 4 Barry (41) 4 Bernard (41) 4 Garry (41) 7 Stephen (39)
Modified ranking: 1 Solomon (44) 3 Errol (42) 3 Jason (42) 6 Barry (41) 6 Bernard (41) 6 Garry (41) 7 Stephen (39)
Dense ranking: 1 Solomon (44) 2 Errol (42) 2 Jason (42) 3 Barry (41) 3 Bernard (41) 3 Garry (41) 4 Stephen (39)
Ordinal ranking: 1 Solomon (44) 2 Errol (42) 3 Jason (42) 4 Barry (41) 5 Bernard (41) 6 Garry (41) 7 Stephen (39)
Fractional ranking: 1.0 Solomon (44) 2.5 Errol (42) 2.5 Jason (42) 5.0 Barry (41) 5.0 Bernard (41) 5.0 Garry (41) 7.0 Stephen (39)"</lang>
AutoHotkey
<lang 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% }</lang> Example:<lang AutoHotkey>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</lang>
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
This uses separate files for each method of ranking: <lang awk>##
- 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()} </lang>
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. <lang C>
- 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; } </lang> 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#
<lang csharp>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();
}
}
}</lang>
- Output:
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
C++
<lang cpp>#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;
}</lang>
- Output:
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
Cowgol
<lang cowgol>include "cowgol.coh";
- List of competitors
record Competitor is
score: uint8; name: [uint8];
end record;
var cs: Competitor[] := {
{44, "Solomon"},
{42, "Jason"},
{42, "Errol"},
{41, "Garry"},
{41, "Bernard"},
{41, "Barry"},
{39, "Stephen"}
};
- Rank competitors given ranking method
interface Ranking(c: [Competitor],
n: intptr,
len: intptr,
last: uint16): (rank: uint16);
sub Rank(cs: [Competitor], num: intptr, r: Ranking) is
var last: uint16 := 0;
var idx: intptr := 0;
while idx < num loop
last := r(cs, idx, num, last);
if last < 100 then
print_i16(last);
else
# print fixed-point rank nicely
print_i16(last / 100);
print_char('.');
print_i16((last % 100) / 10);
print_i16(last % 10);
end if;
print(". ");
print_i8(cs.score);
print(", ");
print(cs.name);
print_nl();
idx := idx + 1;
cs := @next cs;
end loop;
end sub;
- Standard ranking
var stdcount: uint16 := 0; sub Standard implements Ranking is
if n==0 then stdcount := 0; end if;
stdcount := stdcount + 1;
if n>0 and c.score == [@prev c].score then
rank := last;
else
rank := stdcount;
end if;
end sub;
- Modified ranking
sub Modified implements Ranking is
rank := last;
if n == 0 or c.score != [@prev c].score then
while n < len loop
rank := rank + 1;
c := @next c;
if c.score != [@prev c].score then
break;
end if;
n := n + 1;
end loop;
end if;
end sub;
- Dense ranking
sub Dense implements Ranking is
if n>0 and c.score == [@prev c].score then
rank := last;
else
rank := last + 1;
end if;
end sub;
- Ordinal ranking
sub Ordinal implements Ranking is
rank := last + 1;
end sub;
- Fractional ranking (with fixed point arithmetic)
sub Fractional implements Ranking is
rank := last;
if n==0 or c.score != [@prev c].score then
var sum: uint16 := 0;
var ct: uint16 := 0;
while n < len loop
sum := sum + (n as uint16 + 1);
ct := ct + 1;
c := @next c;
if c.score != [@prev c].score then
break;
end if;
n := n + 1;
end loop;
rank := (sum * 100) / (ct as uint16);
end if;
end sub;
record Method is
name: [uint8]; method: Ranking;
end record;
var methods: Method[] := {
{"Standard", Standard},
{"Modified", Modified},
{"Dense", Dense},
{"Ordinal", Ordinal},
{"Fractional", Fractional}
};
var n: @indexof methods := 0; while n < @sizeof methods loop
print("--- ");
print(methods[n].name);
print(" ---\n");
Rank(&cs[0], @sizeof cs, methods[n].method);
print_nl();
n := n + 1;
end loop;</lang>
- Output:
--- 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 --- 1.00. 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
D
<lang 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;
}</lang>
- Output:
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
<lang elixir>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</lang>
- Output:
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
<lang factor>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</lang>
- 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+1/2 42 Jason
2+1/2 42 Errol
5 41 Garry
5 41 Bernard
5 41 Barry
7 39 Stephen
Go
<lang 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) }</lang>
- Output:
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
<lang 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</lang>
- Output:
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:
<lang J>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,.]'</lang>
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:
<lang J> 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│ └───┴──┴───────┘</lang>
Java
<lang java>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]);
}
}
}</lang>
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)
<lang JavaScript>(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');
})();</lang>
- Output:
| 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
<lang JavaScript>((() => {
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');
}))();</lang>
| 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 |
- Output:
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. <lang jq>
- 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 ;</lang>Task<lang jq>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 </lang>
- Output:
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. <lang Julia> function ties{T<:Real}(a::Array{T,1})
unique(a[2:end][a[2:end] .== a[1:end-1]])
end
</lang>
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 <lang Julia> 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 </lang>
Modified Ranking Function <lang Julia> function rankmodified{T<:Real}(a::Array{T,1})
indexin(a, a)
end </lang>
Dense Ranking Function <lang Julia> function rankdense{T<:Real}(a::Array{T,1})
indexin(a, unique(a))
end </lang>
Ordinal Ranking Function <lang Julia> function rankordinal{T<:Real}(a::Array{T,1})
collect(1:length(a))
end </lang> 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 <lang Julia> 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 </lang>
Main <lang Julia> 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 </lang>
- Output:
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
<lang scala>// 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)
}</lang>
- 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: 1.00 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
<lang 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[dataAll, 1, type]},
data}}, First], Alignment->Left], type<>" ranking:", Top]
Grid@{fmtRankedData[data, #] & /@ {"standard", "modified", "dense",
"ordinal", "fractional"}}
</lang>
- Output:
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
Modula-2
<lang modula2>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.</lang>
- Output:
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.
<lang parigp>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)</lang>
- Output:
%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
<lang perl>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 $result;
}
print "Standard:\n" . standard(%scores) . "\n"; print "Modified:\n" . modified(%scores) . "\n"; print "Dense:\n" . dense(%scores) . "\n"; print "Ordinal:\n" . ordinal(%scores) . "\n"; print "Fractional:\n" . fractional(%scores) . "\n";</lang>
- Output:
Standard: 1 Solomon 2 Errol, Jason 4 Barry, Bernard, Garry 7 Stephen Modified: 1 Solomon 3 Errol, Jason 6 Barry, Bernard, Garry 7 Stephen Dense: 1 Solomon 2 Errol, Jason 3 Barry, Bernard, Garry 4 Stephen Ordinal: 1 Solomon 2 Errol 3 Jason 4 Barry 5 Bernard 6 Garry 7 Stephen Fractional: 1.0 Solomon 2.5 Errol, Jason 5.0 Barry, Bernard, Garry 7.0 Stephen
Phix
<lang Phix>function ties(sequence scores)
sequence t = {}, -- {start,num} pairs
tdx = repeat(0,length(scores))
integer last = -1
for i=1 to length(scores) do
integer this = scores[i][1]
if this=last then
t[$][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</lang>
- Output:
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
<lang 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
}
}
}
} </lang> <lang PowerShell> $scores = "44 Solomon","42 Jason","42 Errol","41 Garry","41 Bernard","41 Barry","39 Stephen" </lang> <lang PowerShell> $scores | Get-Ranking -Standard </lang>
- Output:
Name Score Rank ---- ----- ---- Solomon 44 1 Jason 42 2 Errol 42 2 Garry 41 4 Bernard 41 4 Barry 41 4 Stephen 39 7
<lang PowerShell> $scores | Get-Ranking -Modified </lang>
- Output:
Name Score Rank ---- ----- ---- Solomon 44 1 Jason 42 3 Errol 42 3 Garry 41 6 Bernard 41 6 Barry 41 6 Stephen 39 7
<lang PowerShell> $scores | Get-Ranking -Dense </lang>
- Output:
Name Score Rank ---- ----- ---- Solomon 44 1 Jason 42 2 Errol 42 2 Garry 41 3 Bernard 41 3 Barry 41 3 Stephen 39 4
<lang PowerShell> $scores | Get-Ranking -Ordinal </lang>
- Output:
Name Score Rank ---- ----- ---- Solomon 44 1 Jason 42 2 Errol 42 3 Garry 41 4 Bernard 41 5 Barry 41 6 Stephen 39 7
<lang PowerShell> $scores | Get-Ranking -Fractional </lang>
- Output:
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
<lang 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))</lang>
- Output:
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
<lang 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))</lang>
- Output:
Function: #<procedure:rank-function:Standard> 1 44 Solomon = 2 42 Jason = 2 42 Errol = 4 41 Garry = 4 41 Bernard = 4 41 Barry 7 39 Stephen Function: #<procedure:rank-function:Modified> 1 44 Solomon = 3 42 Jason = 3 42 Errol = 6 41 Garry = 6 41 Bernard = 6 41 Barry 7 39 Stephen Function: #<procedure:rank-function:Dense> 1 44 Solomon = 2 42 Jason = 2 42 Errol = 3 41 Garry = 3 41 Bernard = 3 41 Barry 4 39 Stephen Function: #<procedure:rank-function:Ordinal> 1 44 Solomon = 2 42 Jason = 3 42 Errol = 4 41 Garry = 5 41 Bernard = 6 41 Barry 7 39 Stephen Function: #<procedure:rank-function:Fractional> 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
Raku
(formerly Perl 6) <lang 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;</lang>
- Output:
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"]
REXX
<lang 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'</lang>
- Output:
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
<lang 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</lang>
- Output:
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. <lang 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")
}</lang>
- Output:
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
<lang 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))</lang>
- Output:
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
<lang 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"
}
}</lang>
- Output:
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
<lang 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 </lang>
- Output:
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
<lang 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));
}
}</lang> <lang 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);</lang>
- Output:
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)