Find the most common entry in an array

Question

You are given a 32-bit unsigned integer array with length up to 2³², with the property that more than half of the entries in the array are equal to N, for some 32

Answer 1

Proof of correctness for buti-oxa / Jason Hernandez's answer, assuming Jason's answer is the same as buti-oxa's answer and both work the way the algorithm described should work:

We define adjusted suspicion strength as being equal to suspicion strength if top value is selected or -suspicion strength if top value is not selected. Every time you pick the right number, the current adjusted suspicion strength increases by 1. Each time you pick a wrong number, it either drops by 1 or increases by 1, depending on if the wrong number is currently selected. So, the minimum possible ending adjusted suspicion strength is equal to number-of[top values] - number-of[other values]