stable and fast

In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if:

In other words, a matching is stable when there does not exist any pair (A, B) which both prefer each other to their current partner under the matching.
The stable marriage problem has been stated as follows:

Given n men and n women, where each person has ranked all members of the opposite *** in order of preference, marry the men and women together such that there are no two people of opposite *** who would both rather have each other than their current partners. When there are no such pairs of people, the set of marriages is deemed stable.
The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem.

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