(a) In the notes, we show that the stable matching algorithm terminates in at most n² days. Prove the following stronger result: the stable matching algorithm will always terminate in at most (n-1)²+1=n²-2n+2 days.

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Concept of Randomized Approximation Algorithms

Randomized algorithms are algorithms that use random numbers to determine what to do next at any point in their logic. This means that it uses randomization for operation in the logic. Due to this randomness, the time and space complexity of the standard algorithm is reduced.