Ranking methods: Difference between revisions
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7.00 39 Stephen
</pre>
=={{header|Ksh}}==
<lang ksh>
#!/bin/ksh
exec 2> /tmp/Ranking_methods.err
# Ranking methods
#
# # 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)
# # Variables:
#
typeset -a arr=( '44 Solomon' '42 Jason' '42 Errol' '41 Garry' '41 Bernard' '41 Barry' '39 Stephen' )
integer i
# # Functions:
#
# # Function _rankStandard(arr, rankarr) - retun arr with standard ranking
#
function _rankStandard {
typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf
integer _i _j _scr _currank=1 _prevscr
typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do
_scr=${arr[_i]%\ *}
if (( _i>0 )) && (( _scr != _prevscr )); then
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
(( _currank+=${#_shelf[*]} ))
unset _shelf ; typeset -a _shelf
fi
_shelf+=( "${arr[_i]}" )
_prevscr=${_scr}
done
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
}
# # Function _rankModified(arr, rankarr) - retun arr with modified ranking
#
function _rankModified {
typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf
integer _i _j _scr _currank=0 _prevscr
typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do
_scr=${arr[_i]%\ *}
if (( _i>0 )) && (( _scr != _prevscr )); then
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
unset _shelf ; typeset -a _shelf
fi
_shelf+=( "${arr[_i]}" )
(( _currank++ ))
_prevscr=${_scr}
done
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
}
# # Function _rankDense(arr, rankarr) - retun arr with dense ranking
#
function _rankDense {
typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf
integer _i _j _scr _currank=0 _prevscr
typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do
_scr=${arr[_i]%\ *}
if (( _i>0 )) && (( _scr != _prevscr )); then
(( _currank++ ))
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
unset _shelf ; typeset -a _shelf
fi
_shelf+=( "${arr[_i]}" )
_prevscr=${_scr}
done
(( _currank++ ))
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
}
# # Function _rankOrdinal(arr, rankarr) - retun arr with ordinal ranking
#
function _rankOrdinal {
typeset _ranked ; nameref _ranked="$1"
typeset _i ; integer _i
for ((_i=0; _i<${#arr[*]}; _i++)); do
_ranked+=( "$(( _i + 1 )) ${arr[_i]}" )
done
}
# # Function _rankFractional(arr, rankarr) - retun arr with Fractional ranking
#
function _rankFractional {
typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf
integer _i _j _scr _prevscr
typeset -F1 _currank=1.0
typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do
_scr=${arr[_i]%\ *}
if (( _i>0 )) && (( _scr != _prevscr )); then
(( _currank/=${#_shelf[*]} ))
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
_currank=0.0
unset _shelf ; typeset -a _shelf
fi
(( _i>0 )) && (( _currank+=_i + 1 ))
_shelf+=( "${arr[_i]}" )
_prevscr=${_scr}
done
for ((_j=0; _j<${#_shelf[*]}; _j++)); do
(( _currank/=${#_shelf[*]} ))
_ranked+=( "${_currank} ${_shelf[_j]}" )
done
}
######
# main #
######
printf "\n\nInput Data: ${#arr[*]} records\n---------------------\n"
for ((i=0; i< ${#arr[*]}; i++)); do
print ${arr[i]}
done
typeset -a rankedarr
_rankStandard rankedarr
printf "\n\nStandard Ranking\n----------------\n"
for ((i=0; i< ${#rankedarr[*]}; i++)); do
print ${rankedarr[i]}
done
unset rankedarr ; typeset -a rankedarr
_rankModified rankedarr
printf "\n\nModified Ranking\n----------------\n"
for ((i=0; i< ${#rankedarr[*]}; i++)); do
print ${rankedarr[i]}
done
unset rankedarr ; typeset -a rankedarr
_rankDense rankedarr
printf "\n\nDense Ranking\n-------------\n"
for ((i=0; i< ${#rankedarr[*]}; i++)); do
print ${rankedarr[i]}
done
unset rankedarr ; typeset -a rankedarr
_rankOrdinal rankedarr
printf "\n\nOrdinal Ranking\n---------------\n"
for ((i=0; i< ${#rankedarr[*]}; i++)); do
print ${rankedarr[i]}
done
unset rankedarr ; typeset -a rankedarr
_rankFractional rankedarr
printf "\n\nFractional Ranking\n------------------\n"
for ((i=0; i< ${#rankedarr[*]}; i++)); do
print ${rankedarr[i]}
done</lang>
{{out}}<pre>
Input Data: 7 records
---------------------
44 Solomon
42 Jason
42 Errol
41 Garry
41 Bernard
41 Barry
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
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</pre>
=={{header|M2000 Interpreter}}==
|
Revision as of 16:03, 5 November 2021
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
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.
11l
<lang 11l>F mc_rank([(Int, String)] iterable)
‘Modified competition ranking’ [(Float, (Int, String))] r V lastresult = -1 [(Int, String)] fifo L(item) iterable I item[0] == lastresult fifo [+]= item E V n = L.index L !fifo.empty r.append((n, fifo.pop(0))) lastresult = item[0] fifo [+]= item L !fifo.empty r.append((iterable.len, fifo.pop(0))) R r
F sc_rank([(Int, String)] iterable)
‘Standard competition ranking’ [(Float, (Int, String))] r V lastresult = -1 V lastrank = -1 L(item) iterable I item[0] == lastresult r.append((lastrank, item)) E V n = L.index + 1 r.append((n, item)) lastresult = item[0] lastrank = n R r
F d_rank([(Int, String)] iterable)
‘Dense ranking’ [(Float, (Int, String))] r V lastresult = -1 V lastrank = 0 L(item) iterable I item[0] == lastresult r.append((lastrank, item)) E lastresult = item[0] lastrank++ r.append((lastrank, item)) R r
F o_rank([(Int, String)] iterable)
‘Ordinal ranking’ R enumerate(iterable, 1).map((i, item) -> ((Float(i), item)))
F f_rank([(Int, String)] iterable)
‘Fractional ranking’ [(Float, (Int, String))] r V last = -1 [(Int, (Int, String))] fifo L(item) iterable I item[0] != last I !fifo.empty V mean = Float(sum(fifo.map(f -> f[0]))) / fifo.len L !fifo.empty r.append((mean, fifo.pop(0)[1])) last = item[0] fifo.append((L.index + 1, item)) I !fifo.empty V mean = sum(fifo.map(f -> f[0])) / fifo.len L !fifo.empty r.append((mean, fifo.pop(0)[1])) R r
V scores = [(44, ‘Solomon’),
(42, ‘Jason’), (42, ‘Errol’), (41, ‘Garry’), (41, ‘Bernard’), (41, ‘Barry’), (39, ‘Stephen’)]
print("\nScores to be ranked (best first):") L(n, s) scores
print(‘ #2 #.’.format(n, s))
L(ranker, ranking_method) [(sc_rank, ‘Standard competition ranking’),
(mc_rank, ‘Modified competition ranking’), (d_rank, ‘Dense ranking’), (o_rank, ‘Ordinal ranking’), (f_rank, ‘Fractional ranking’)] print("\n#.:".format(ranking_method)) L(rank, score) ranker(scores) print(‘ #3, (#., #.)’.format(rank, score[0], score[1]))</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)
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
APL
These functions each take a 2-by-N matrix, where the first column contains the score, and the second column contains the name. They return a 3-by-N matrix, with the ranking added.
<lang apl>standard ← ∊∘(⌊\¨⊢⊂⍳∘≢)∘(1,2≠/⊢)∘(1⌷[2]⊢),⊢ modified ← ∊∘(⌈\∘⌽¨⊢⊂⍳∘≢)∘(1,2≠/⊢)∘(1⌷[2]⊢),⊢ dense ← (+\1,2≠/1⌷[2]⊢),⊢ ordinal ← ⍳∘≢,⊢ fractional ← ∊∘((≢(/∘⊢)+/÷≢)¨⊢⊂⍳∘≢)∘(1,2≠/⊢)∘(1⌷[2]⊢),⊢</lang>
- Output:
⍝ Input scores table from task: scores←⍉⍪44,⊂'Solomon' scores⍪←42,⊂'Jason' scores⍪←42,⊂'Errol' scores⍪←41,⊂'Garry' scores⍪←41,⊂'Bernard' scores⍪←41,⊂'Barry' scores⍪←39,⊂'Stephen' ⍝ Apply each function to it standard scores 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen modified scores 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen dense scores 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen ordinal scores 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen fractional scores 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 = $1 lastrank = FNR}
} //{sc_rank()} </lang>
The input as a file ranking.txt
:
44 Solomon 42 Jason 42 Errol 41 Garry 41 Bernard 41 Barry 39 Stephen
- Output:
C:\Users\RC\Code>awk -f ranking_sc.awk ranking.txt 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen C:\Users\RC\Code>awk -f ranking_mc.awk ranking.txt 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen C:\Users\RC\Code>awk -f ranking_d.awk ranking.txt 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen C:\Users\RC\Code>awk -f ranking_o.awk ranking.txt 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen C:\Users\RC\Code>awk -f ranking_f.awk ranking.txt 1 44 Solomon 2.5 42 Jason 2.5 42 Errol 5 41 Garry 5 41 Bernard 5 41 Barry 7 39 Stephen C:\Users\RC\Code>
BASIC
<lang BASIC>10 READ N 20 DIM S(N),N$(N),R(N) 30 FOR I=1 TO N: READ S(I),N$(I): NEXT 40 PRINT "--- Standard ranking ---": GOSUB 100: GOSUB 400 50 PRINT "--- Modified ranking ---": GOSUB 150: GOSUB 400 60 PRINT "--- Dense ranking ---": GOSUB 200: GOSUB 400 70 PRINT "--- Ordinal ranking ---": GOSUB 250: GOSUB 400 80 PRINT "--- Fractional ranking ---": GOSUB 300: GOSUB 400 90 END 100 REM 101 REM ** Ordinal ranking ** 110 R(1)=1 120 FOR I=2 TO N 130 IF S(I)=S(I-1) THEN R(I)=R(I-1) ELSE R(I)=I 140 NEXT: RETURN 150 REM 151 REM ** Modified ranking ** 160 R(N)=N 170 FOR I=N-1 TO 1 STEP -1 180 IF S(I)=S(I+1) THEN R(I)=R(I+1) ELSE R(I)=I 190 NEXT: RETURN 200 REM 201 REM ** Dense ranking ** 210 R(1)=1 220 FOR I=2 TO N: R(I)=R(I-1)-(S(I)<>S(I-1)): NEXT 230 RETURN 250 REM 251 REM ** Ordinal ranking ** 260 FOR I=1 TO N: R(I)=I: NEXT: RETURN 300 REM 301 REM ** Fractional ranking ** 310 I=1: J=2 320 IF J<=N THEN IF S(J-1)=S(J) THEN J=J+1: GOTO 320 330 FOR K=I TO J-1: R(K) = (I+J-1)/2: NEXT 340 I=J: J=J+1: IF I<=N THEN 320 350 RETURN 400 REM 401 REM ** Print the table *** 410 FOR I=1 TO N 420 PRINT USING "\ \ ##, \ \";STR$(R(I));S(I);N$(I) 430 NEXT 440 PRINT: RETURN 500 DATA 7 510 DATA 44,Solomon 520 DATA 42,Jason 530 DATA 42,Errol 540 DATA 41,Garry 550 DATA 41,Bernard 560 DATA 41,Barry 570 DATA 39,Stephen</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
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
FreeBASIC
<lang freebasic> Data 44,"Solomon", 42,"Jason", 42,"Errol", 41,"Garry" Data 41,"Bernard", 41,"Barry", 39,"Stephen"
Dim Shared As Integer n = 7 Dim Shared As Integer puntos(n), i Dim Shared As Single ptosnom(n) Dim Shared As String nombre(n)
Print "Puntuaciones a clasificar (mejores primero):" For i = 1 To n
Read puntos(i), nombre(i) Print Using " ##, \ \"; puntos(i); nombre(i)
Next i Print
Sub MostarTabla
For i = 1 To n Print Using " \ \ ##, \ \"; Str(ptosnom(i)); puntos(i); nombre(i) Next i Print
End Sub
Print "--- Standard ranking ---" ptosnom(1) = 1 For i = 2 To n
If puntos(i) = puntos(i-1) Then ptosnom(i) = ptosnom(i-1) Else ptosnom(i) = i
Next i MostarTabla
Print "--- Modified ranking ---"
ptosnom(n) = n
For i = n-1 To 1 Step -1
If puntos(i) = puntos(i+1) Then ptosnom(i) = ptosnom(i+1) Else ptosnom(i) = i
Next i MostarTabla
Print "--- Dense ranking ---" ptosnom(1) = 1 For i = 2 To n
ptosnom(i) = ptosnom(i-1) - (puntos(i) <> puntos(i-1))
Next i MostarTabla
Print "--- Ordinal ranking ---" For i = 1 To n
ptosnom(i) = i
Next i MostarTabla
Print "--- Fractional ranking ---" i = 1 Dim As Integer j = 2 Do
If j <= n Then If (puntos(j-1) = puntos(j)) Then j += 1 For k As Integer = i To j-1 ptosnom(k) = (i+j-1) / 2 Next k i = j j += 1
Loop While i <= n MostarTabla Sleep </lang>
- Output:
Puntuaciones a clasificar (mejores primero): 44 Solomon 42 Jason 42 Errol 41 Garry 41 Bernard 41 Barry 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 --- 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 4.5 41 Garry 4.5 41 Bernard 6 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
Ksh
<lang ksh>
- !/bin/ksh
exec 2> /tmp/Ranking_methods.err
- Ranking methods
- # 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)
- # Variables:
typeset -a arr=( '44 Solomon' '42 Jason' '42 Errol' '41 Garry' '41 Bernard' '41 Barry' '39 Stephen' ) integer i
- # Functions:
- # Function _rankStandard(arr, rankarr) - retun arr with standard ranking
function _rankStandard { typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf integer _i _j _scr _currank=1 _prevscr typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do _scr=${arr[_i]%\ *} if (( _i>0 )) && (( _scr != _prevscr )); then for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done (( _currank+=${#_shelf[*]} )) unset _shelf ; typeset -a _shelf fi _shelf+=( "${arr[_i]}" ) _prevscr=${_scr} done for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done }
- # Function _rankModified(arr, rankarr) - retun arr with modified ranking
function _rankModified { typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf integer _i _j _scr _currank=0 _prevscr typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do _scr=${arr[_i]%\ *} if (( _i>0 )) && (( _scr != _prevscr )); then for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done unset _shelf ; typeset -a _shelf fi _shelf+=( "${arr[_i]}" ) (( _currank++ )) _prevscr=${_scr} done for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done }
- # Function _rankDense(arr, rankarr) - retun arr with dense ranking
function _rankDense { typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf integer _i _j _scr _currank=0 _prevscr typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do _scr=${arr[_i]%\ *} if (( _i>0 )) && (( _scr != _prevscr )); then (( _currank++ )) for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done unset _shelf ; typeset -a _shelf fi _shelf+=( "${arr[_i]}" ) _prevscr=${_scr} done (( _currank++ )) for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done }
- # Function _rankOrdinal(arr, rankarr) - retun arr with ordinal ranking
function _rankOrdinal { typeset _ranked ; nameref _ranked="$1" typeset _i ; integer _i
for ((_i=0; _i<${#arr[*]}; _i++)); do _ranked+=( "$(( _i + 1 )) ${arr[_i]}" ) done }
- # Function _rankFractional(arr, rankarr) - retun arr with Fractional ranking
function _rankFractional { typeset _ranked ; nameref _ranked="$1"
typeset _i _j _scr _currank _prevscr _shelf integer _i _j _scr _prevscr typeset -F1 _currank=1.0 typeset -a _shelf
for ((_i=0; _i<${#arr[*]}; _i++)); do _scr=${arr[_i]%\ *} if (( _i>0 )) && (( _scr != _prevscr )); then (( _currank/=${#_shelf[*]} )) for ((_j=0; _j<${#_shelf[*]}; _j++)); do _ranked+=( "${_currank} ${_shelf[_j]}" ) done _currank=0.0 unset _shelf ; typeset -a _shelf fi (( _i>0 )) && (( _currank+=_i + 1 )) _shelf+=( "${arr[_i]}" ) _prevscr=${_scr} done for ((_j=0; _j<${#_shelf[*]}; _j++)); do (( _currank/=${#_shelf[*]} )) _ranked+=( "${_currank} ${_shelf[_j]}" ) done }
######
- main #
######
printf "\n\nInput Data: ${#arr[*]} records\n---------------------\n" for ((i=0; i< ${#arr[*]}; i++)); do print ${arr[i]} done
typeset -a rankedarr _rankStandard rankedarr printf "\n\nStandard Ranking\n----------------\n" for ((i=0; i< ${#rankedarr[*]}; i++)); do print ${rankedarr[i]} done
unset rankedarr ; typeset -a rankedarr _rankModified rankedarr printf "\n\nModified Ranking\n----------------\n" for ((i=0; i< ${#rankedarr[*]}; i++)); do print ${rankedarr[i]} done
unset rankedarr ; typeset -a rankedarr _rankDense rankedarr printf "\n\nDense Ranking\n-------------\n" for ((i=0; i< ${#rankedarr[*]}; i++)); do print ${rankedarr[i]} done
unset rankedarr ; typeset -a rankedarr _rankOrdinal rankedarr printf "\n\nOrdinal Ranking\n---------------\n" for ((i=0; i< ${#rankedarr[*]}; i++)); do print ${rankedarr[i]} done
unset rankedarr ; typeset -a rankedarr _rankFractional rankedarr printf "\n\nFractional Ranking\n------------------\n" for ((i=0; i< ${#rankedarr[*]}; i++)); do print ${rankedarr[i]} done</lang>
- Output:
Input Data: 7 records --------------------- 44 Solomon 42 Jason 42 Errol 41 Garry 41 Bernard 41 Barry 39 Stephen
Standard Ranking ---------------- 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen
Modified Ranking ---------------- 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen
Dense Ranking ------------- 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen
Ordinal Ranking --------------- 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen
Fractional Ranking ------------------ 1.0 44 Solomon 2.5 42 Jason 2.5 42 Errol 5.0 41 Garry 5.0 41 Bernard 5.0 41 Barry
7.0 39 Stephen
M2000 Interpreter
<lang M2000 Interpreter> Module Ranking (output$, orderlist) { Open output$ for output as #k Gosub getdata Print #k, "Standard ranking:" skip=true rankval=1 oldrank=0 For i=1 to items Read rank, name$ if skip then skip=false else.if oldrank<>rank then rankval=i end if oldrank=rank Print #k, Format$("{0::-5} {2} ({1})", rankval, rank, name$) Next Gosub getdata Print #k, "Modified ranking:" skip=true rankval=Items oldrank=0 ShiftBack 1, -items*2 ' reverse stack items For i=items to 1 Read name$, rank if skip then skip=false else.if oldrank<>rank then rankval=i end if oldrank=rank Data Format$("{0::-5} {2} ({1})", rankval, rank, name$) Next ShiftBack 1, -items ' reverse stack items For i=1 to items Print #k, letter$ Next i Gosub getdata Print #k, "Dense ranking:" skip=true Dense=Stack acc=1 oldrank=0 For i=1 to items Read rank, name$ if skip then skip=false oldrank=rank else.if oldrank<>rank then oldrank=rank Gosub dense acc=i end if Stack Dense {data Format$(" {0} ({1})",name$, rank)} Next Gosub dense Gosub getdata Print #k, "Ordinal ranking:" For i=1 to items Print #k, Format$("{0::-5} {2} ({1})", i, Number, letter$) Next Gosub getdata Print #k, "Fractional ranking:" skip=true Frac=Stack acc=1 oldrank=0 For i=1 to items Read rank, name$ if skip then skip=false oldrank=rank else.if oldrank<>rank then oldrank=rank Gosub Fractional acc=I end if Stack Frac {data Format$(" {0} ({1})",name$, rank)} Next Gosub Fractional Close #k End Fractional: val=((len(Frac)+1)/2+(acc-1)) Stack Frac { while not empty Print #k, format$("{0:1:-5}{1}", val, letter$) end while } Return dense: Stack Dense { while not empty Print #k, format$("{0::-5}{1}", acc, letter$) end while } Return getdata: flush stack stack(orderlist) // place a copy of items to current stack items=stack.size/2 Return } Flush Data 44, "Solomon", 42, "Jason", 42, "Errol" Data 41, "Garry", 41, "Bernard", 41, "Barry" Data 39, "Stephen" // get all items from current stack to a new stack alist=[] // To screen Ranking "", alist // To file Ranking "ranking.txt", alist </lang>
- Output:
Standard ranking: 1 Solomon (44) 2 Jason (42) 2 Errol (42) 4 Garry (41) 4 Bernard (41) 4 Barry (41) 7 Stephen (39) Modified ranking: 1 Solomon (44) 3 Jason (42) 3 Errol (42) 6 Garry (41) 6 Bernard (41) 6 Barry (41) 7 Stephen (39) Dense ranking: 1 Solomon (44) 2 Jason (42) 2 Errol (42) 4 Garry (41) 4 Bernard (41) 4 Barry (41) 7 Stephen (39) Ordinal ranking: 1 Solomon (44) 2 Jason (42) 3 Errol (42) 4 Garry (41) 5 Bernard (41) 6 Barry (41) 7 Stephen (39) Fractional ranking: 1.0 Solomon (44) 2.5 Jason (42) 2.5 Errol (42) 5.0 Garry (41) 5.0 Bernard (41) 5.0 Barry (41) 7.0 Stephen (39)
Mathematica/Wolfram Language
<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
Nim
Using an auxiliary table
To simplify, it’s convenient to build a table giving for each score the list of competitor names. <lang Nim>import algorithm, sequtils, stats, tables
type
Record = tuple[score: int; name: string] # Input data. Groups = OrderedTable[int, seq[string]] # Maps score to list of names. Rank = tuple[rank: int; name: string; score: int] # Result. FractRank = tuple[rank: float; name: string; score: int] # Result (fractional).
func cmp(a, b: (int, seq[string])): int =
## Comparison function needed to sort the groups. cmp(a[0], b[0])
func toGroups(records: openArray[Record]): Groups =
## Build a "Groups" table from the records. for record in records: result.mgetOrPut(record.score, @[]).add record.name # Sort the list of names by alphabetic order. for score in result.keys: sort(result[score]) # Sort the groups by decreasing score. result.sort(cmp, Descending)
func standardRanks(groups: Groups): seq[Rank] =
var rank = 1 for score, names in groups.pairs: for name in names: result.add (rank, name, score) inc rank, names.len
func modifiedRanks(groups: Groups): seq[Rank] =
var rank = 0 for score, names in groups.pairs: inc rank, names.len for name in names: result.add (rank, name, score)
func denseRanks(groups: Groups): seq[Rank] =
var rank = 0 for score, names in groups.pairs: inc rank for name in names: result.add (rank, name, score)
func ordinalRanks(groups: Groups): seq[Rank] =
var rank = 0 for score, names in groups.pairs: for name in names: inc rank result.add (rank, name, score)
func fractionalRanks(groups: Groups): seq[FractRank] =
var rank = 1 for score, names in groups.pairs: let fRank = mean(toSeq(rank..(rank + names.high))) for name in names: result.add (fRank, name, score) inc rank, names.len
when isMainModule:
const Data = [(44, "Solomon"), (42, "Jason"), (42, "Errol"), (41, "Garry"), (41, "Bernard"), (41, "Barry"), (39, "Stephen")]
let groups = Data.toGroups() echo "Standard ranking:" for (rank, name, score) in groups.standardRanks(): echo rank, ": ", name, " ", score
echo() echo "Modified ranking:" for (rank, name, score) in groups.modifiedRanks(): echo rank, ": ", name, " ", score
echo() echo "Dense ranking:" for (rank, name, score) in groups.denseRanks(): echo rank, ": ", name, " ", score
echo() echo "Ordinal ranking:" for (rank, name, score) in groups.ordinalRanks(): echo rank, ": ", name, " ", score
echo() echo "Fractional ranking:" for (rank, name, score) in groups.fractionalRanks(): echo rank, ": ", name, " ", score</lang>
- Output:
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
Without an auxiliary table
But it is possible to do the ranking without an auxiliary table. <lang Nim>import algorithm
type
Record = tuple[score: int; name: string] # Input data. Rank = tuple[rank: int; name: string; score: int] # Result. FractRank = tuple[rank: float; name: string; score: int] # Result (fractional).
func cmp(a, b: Record): int =
## Record comparison function (needed for sorting). result = cmp(b[0], a[0]) # Reverse order. if result == 0: result = cmp(a.name, b.name) # Alphabetical order.
func standardRanks(records: openArray[Record]): seq[Rank] =
let records = sorted(records, cmp) var rank = 1 var currScore = records[0].score for idx, (score, name) in records: if score != currScore: rank = idx + 1 currScore = score result.add (rank, name, score)
func modifiedRanks(records: openArray[Record]): seq[Rank] =
let records = sorted(records, cmp) var rank = records.len var currScore = records[^1].score for idx in countdown(records.high, 0): let (score, name) = records[idx] if score != currScore: rank = idx + 1 currScore = score result.add (rank, name, score) result.reverse()
func denseRanks(records: openArray[Record]): seq[Rank] =
let records = sorted(records, cmp) var rank = 1 var currScore = records[0].score for (score, name) in records: if score != currScore: inc rank currScore = score result.add (rank, name, score)
func ordinalRanks(records: openArray[Record]): seq[Rank] =
let records = sorted(records, cmp) var rank = 0 for (score, name) in records: inc rank result.add (rank, name, score)
func fractionalRanks(records: openArray[Record]): seq[FractRank] =
let records = sorted(records, cmp) # Build a list of ranks. var currScore = records[0].score var sum = 0 var ranks: seq[float] var count = 0 for idx, record in records: if record.score == currScore: inc count inc sum, idx + 1 else: ranks.add sum / count count = 1 currScore = record.score sum = idx + 1 ranks.add sum / count
# Give a rank to each record. currScore = records[0].score var rankIndex = 0 for (score, name) in records: if score != currScore: inc rankIndex currScore = score result.add (ranks[rankIndex], name, score)
when isMainModule:
const Data = [(44, "Solomon"), (42, "Jason"), (42, "Errol"), (41, "Garry"), (41, "Bernard"), (41, "Barry"), (39, "Stephen")]
echo "Standard ranking:" for (rank, name, score) in Data.standardRanks(): echo rank, ": ", name, " ", score
echo() echo "Modified ranking:" for (rank, name, score) in Data.modifiedRanks(): echo rank, ": ", name, " ", score
echo() echo "Dense ranking:" for (rank, name, score) in Data.denseRanks(): echo rank, ": ", name, " ", score
echo() echo "Ordinal ranking:" for (rank, name, score) in Data.ordinalRanks(): echo rank, ": ", name, " ", score
echo() echo "Fractional ranking:" for (rank, name, score) in Data.fractionalRanks(): echo rank, ": ", name, " ", score</lang>
- Output:
Same output as with other version.
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$who"
}
}</lang>
- Output:
Using method 'standard'... Rank Score Who 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen Using method 'modified'... Rank Score Who 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen Using method 'dense'... Rank Score Who 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen Using method 'ordinal'... Rank Score Who 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen Using method 'fractional'... Rank Score Who 1 44 Solomon 2.5 42 Jason 2.5 42 Errol 5 41 Garry 5 41 Bernard 5 41 Barry 7 39 Stephen
True BASIC
<lang basic> LET n = 7 DIM puntos(7), ptosnom(7), nombre$(7)
SUB MostarTabla
FOR i = 1 to n PRINT str$(ptosnom(i)); " "; puntos(i); " "; nombre$(i) NEXT i PRINT
END SUB
PRINT "Puntuaciones a clasificar (mejores primero):" FOR i = 1 to n
READ puntos(i), nombre$(i) PRINT " "; puntos(i); " "; nombre$(i)
NEXT i
PRINT PRINT "--- Standard ranking ---" LET ptosnom(1) = 1 FOR i = 2 to n NEXT i CALL MostarTabla
PRINT "--- Modified ranking ---" LET ptosnom(n) = n FOR i = n-1 to 1 step -1
IF puntos(i) = puntos(i+1) then LET ptosnom(i) = ptosnom(i+1) else LET ptosnom(i) = i
NEXT i CALL MostarTabla
PRINT "--- Ordinal ranking ---" FOR i = 1 to n
LET ptosnom(i) = i
NEXT i CALL MostarTabla
PRINT "--- Fractional ranking ---" LET i = 1 LET j = 2 DO
IF j <= n then IF (puntos(j-1) = puntos(j)) then LET j = j + 1 END IF END IF
FOR k = i to j-1 LET ptosnom(k) = (i+j-1) / 2 NEXT k LET i = j LET j = j + 1
LOOP UNTIL i > n CALL MOSTARTABLA
DATA 44, "Solomon", 42, "Jason", 42, "Errol", 41, "Garry", 41, "Bernard", 41, "Barry", 39, "Stephen" END </lang>
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"
Wren
<lang ecmascript>import "/math" for Nums import "/fmt" for Fmt
/* 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
- /
var standardRanking = Fn.new { |scores|
var rankings = List.filled(scores.count, 0) rankings[0] = 1 for (i in 1...scores.count) { rankings[i] = (scores[i][0] == scores[i-1][0]) ? rankings[i-1] : i + 1 } return rankings
}
var modifiedRanking = Fn.new { |scores|
var rankings = List.filled(scores.count, 0) rankings[0] = 1 for (i in 1...scores.count) { rankings[i] = i + 1 var currScore = scores[i][0] for (j in i-1..0) { if (currScore != scores[j][0]) break rankings[j] = i + 1 } } return rankings
}
var denseRanking = Fn.new { |scores|
var rankings = List.filled(scores.count, 0) rankings[0] = 1 var prevRanking = 1 for (i in 1...scores.count) { rankings[i] = (scores[i][0] == scores[i-1][0]) ? prevRanking : (prevRanking = prevRanking+1) } return rankings
}
var ordinalRanking = Fn.new { |scores| (1..scores.count).toList }
var fractionalRanking = Fn.new { |scores|
var rankings = List.filled(scores.count, 0) rankings[0] = 1 for (i in 1...scores.count) { var k = i var currScore = scores[i][0] for (j in i-1..0) { if (currScore != scores[j][0]) break k = j } var avg = Nums.mean(k..i) + 1 for (m in k..i) rankings[m] = avg } return rankings
}
var printRankings = Fn.new { |title, rankings, scores|
System.print(title + ":") for (i in 0...rankings.count) { System.print("%(rankings[i]) %(scores[i][0]) %(scores[i][1])") } System.print()
}
var printFractionalRankings = Fn.new { |title, rankings, scores|
System.print(title + ":") for (i in 0...rankings.count) { Fmt.print("$3.2f $d $s", rankings[i], scores[i][0], scores[i][1]) } System.print()
}
var scores = [[44, "Solomon"], [42, "Jason"], [42, "Errol"], [41, "Garry"],
[41, "Bernard"], [41, "Barry"], [39, "Stephen"]]
printRankings.call("Standard ranking", standardRanking.call(scores), scores) printRankings.call("Modified ranking", modifiedRanking.call(scores), scores) printRankings.call("Dense ranking", denseRanking.call(scores), scores) printRankings.call("Ordinal ranking", ordinalRanking.call(scores), scores) printFractionalRankings.call("Fractional ranking", fractionalRanking.call(scores), scores)</lang>
- Output:
Standard ranking: 1 44 Solomon 2 42 Jason 2 42 Errol 4 41 Garry 4 41 Bernard 4 41 Barry 7 39 Stephen Modified ranking: 1 44 Solomon 3 42 Jason 3 42 Errol 6 41 Garry 6 41 Bernard 6 41 Barry 7 39 Stephen Dense ranking: 1 44 Solomon 2 42 Jason 2 42 Errol 3 41 Garry 3 41 Bernard 3 41 Barry 4 39 Stephen Ordinal ranking: 1 44 Solomon 2 42 Jason 3 42 Errol 4 41 Garry 5 41 Bernard 6 41 Barry 7 39 Stephen Fractional ranking: 1.00 44 Solomon 2.50 42 Jason 2.50 42 Errol 5.00 41 Garry 5.00 41 Bernard 5.00 41 Barry 7.00 39 Stephen
Yabasic
<lang yabasic> n = 7 dim puntos(7), ptosnom(7), nombre$(7)
sub MostarTabla()
for i = 1 to n print str$(ptosnom(i)), " ", puntos(i), " ", nombre$(i) next i print
end sub
print "Puntuaciones a clasificar (mejores primero):" for i = 1 to n
read puntos(i), nombre$(i) print " ", puntos(i), " ", nombre$(i)
next i
print print "--- Standard ranking ---" ptosnom(1) = 1 for i = 2 to n
if puntos(i) = puntos(i-1) then ptosnom(i) = ptosnom(i-1) else ptosnom(i) = i : fi
next i MostarTabla()
print "--- Modified ranking ---" ptosnom(n) = n for i = n-1 to 1 step -1
if puntos(i) = puntos(i+1) then ptosnom(i) = ptosnom(i+1) else ptosnom(i) = i : fi
next i MostarTabla()
print "--- Ordinal ranking ---" for i = 1 to n
ptosnom(i) = i
next i MostarTabla()
print "--- Fractional ranking ---" i = 1 j = 2 repeat
if j <= n then if (puntos(j-1) = puntos(j)) then j = j + 1 : fi end if for k = i to j-1 ptosnom(k) = (i+j-1) / 2 next k i = j j = j + 1
until i > n MostarTabla()
data 44, "Solomon", 42, "Jason", 42, "Errol", 41, "Garry", 41, "Bernard", 41, "Barry", 39, "Stephen" end </lang>
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)
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