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using System;
using System.Collections.Generic;
using System.Linq;
namespace Algorithms.Problems.StableMarriage;
public static class GaleShapley
{
/// <summary>
/// Finds a stable matching between two equal sets of elements (fills EngagedTo properties).
/// time complexity: O(n^2), where n - array size.
/// Guarantees:
/// - Everyone is matched
/// - Matches are stable (there is no better accepter, for any given proposer, which would accept a new match).
/// Presented and proven by David Gale and Lloyd Shapley in 1962.
/// </summary>
public static void Match(Proposer[] proposers, Accepter[] accepters)
{
if (proposers.Length != accepters.Length)
{
throw new ArgumentException("Collections must have equal count");
}
while (proposers.Any(m => !IsEngaged(m)))
{
DoSingleMatchingRound(proposers.Where(m => !IsEngaged(m)));
}
}
private static bool IsEngaged(Proposer proposer) => proposer.EngagedTo is not null;
private static void DoSingleMatchingRound(IEnumerable<Proposer> proposers)
{
foreach (var newProposer in proposers)
{
var accepter = newProposer.PreferenceOrder.First!.Value;
if (accepter.EngagedTo is null)
{
Engage(newProposer, accepter);
}
else
{
if (accepter.PrefersOverCurrent(newProposer))
{
Free(accepter.EngagedTo);
Engage(newProposer, accepter);
}
}
newProposer.PreferenceOrder.RemoveFirst();
}
}
private static void Free(Proposer proposer)
{
proposer.EngagedTo = null;
}
private static void Engage(Proposer proposer, Accepter accepter)
{
proposer.EngagedTo = accepter;
accepter.EngagedTo = proposer;
}
}
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