Consider an execution of the GaleShapley algorithm on n men

Consider an execution of the Gale-Shapley algorithm on n men and n women. If the algorithm makes exactly n+1 proposals before terminating, how many men are assigned their first choice women? Prove your answer correct. Is it possible for two different men to both be assigned their respective last-choice woman? Prove your answer correct.

Solution

O (n2) is best case

Maximum O (n2) men are assigned their first choice women

No, any one will get last choice woman