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In mathematics, economics, and computer science, the stable marriage problem (SMP) is the problem of finding a stable matching between two sets of elements given a set of preferences for each element. In 1962, David Gale and Lloyd Shapley proved that, for any equal number of men and women, it is always possible to solve the SMP and make all marriages stable. Following the algorithm of the prove.

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{` function stableMatching { Initialize all m ∈ M and w ∈ W to free while ∃ free man m who still has a woman w to propose to { w = m's highest ranked woman to whom he has not yet proposed if w is free (m, w) become engaged else some pair (m', w) already exists if w prefers m to m' (m, w) become engaged m' becomes free else (m', w) remain engaged } } `}

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