The Gale-Shapley algorithm is upper bounded by ≤ n^2 for n men and n women, since each man can only make ≤n proposals. However, we haven’t shown a lower bound on number of iterations. To show the lower bound is also in the order of n^2, please give a way to construct the preference lists for n men and n women such that the Gale-Shapley algorithm will run for Θ(n^2) iterations. (For simplicity, you can assume that the algorithm always chooses the unmatched man with the smallest index at each iteration).
The Gale-Shapley
However, we haven’t shown a lower bound on number of iterations. To show the lower bound is also in
the order of n^2, please give a way to construct the preference lists for n men and n women such that the
Gale-Shapley algorithm will run for Θ(n^2) iterations. (For simplicity, you can assume that the algorithm
always chooses the unmatched man with the smallest index at each iteration).
Introduction
An algorithm is a set of instructions or steps used to complete a task or solve a problem. It is a set of logical rules that are created to complete a given task. Algorithms are used in computing to give directions to machines and help them complete tasks in an efficient manner. Algorithms are used across a variety of fields including artificial intelligence, data mining, and natural language processing. Algorithms are also used in problem-solving activities, such as solving a maze or playing a game.
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