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feat: StableMatching Algorithm #1446

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65 changes: 65 additions & 0 deletions Backtracking/StableMatching.js
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Original file line number Diff line number Diff line change
@@ -0,0 +1,65 @@
// This is the Stable Matching Gale Shapley Algorithm
// Gale Shapley describes the method of Stable One to One matching

function initFreeMen() {
for (let man in preferredRankingMen) {
freeMen.push(man);
}
}

function stableMatch() {
while (freeMen.length > 0) {
for (let man of freeMen) {
startMatching(man);
}
}
}

function startMatching(man) {
for (let woman of preferredRankingMen[man]) {
const takenMatch = temporaryEngagement.find((couple) => woman === couple[1]);

if (!takenMatch) {
temporaryEngagement.push([man, woman]);
freeMen = freeMen.filter((m) => m !== man);
break;
} else {
const currentGuy = takenMatch[0];
const currentGuyIndex = preferredRankingWomen[woman].indexOf(currentGuy);
const potentialGuyIndex = preferredRankingWomen[woman].indexOf(man);

if (currentGuyIndex > potentialGuyIndex) {
freeMen = freeMen.filter((m) => m !== man);
freeMen.push(currentGuy);
takenMatch[0] = man;
break;
}
}
}
}

const preferredRankingMen = {
'Alice': ['Frank', 'Eva', 'Dave'],
'Bob': ['Frank', 'Dave', 'Eva'],
'Carol': ['Dave', 'Eva', 'Frank']
};

const preferredRankingWomen = {
'Dave': ['Carol', 'Alice', 'Bob'],
'Eva': ['Alice', 'Bob', 'Carol'],
'Frank': ['Carol', 'Alice', 'Bob']
};

// This will store all the paired men and women
// until the loop ends
// This array will store the current engagements in the format [man, woman]
const temporaryEngagement = [];

// This will store all the men who are yet
// to be paired and are still single
// Initially, all the men are considered free and added to this array.
let freeMen = [];

initFreeMen();
stableMatch();
console.log("Final Matching:", temporaryEngagement);

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