GATE CS 2025 Set 2 Q10 — Searching, Sorting, Hashing

To find an element in an unordered list of $N$ distinct integers ($N \ge 2$) that is NOT the largest, we can use the following approach:

1. Pick any two arbitrary elements from the list, say $a$ and $b$.
2. Compare them:
   • If $a < b$, then $a$ cannot be the largest element in the list because $b$ is already larger than $a$. Thus, $a$ is guaranteed to not be the largest.
   • If $a > b$, then $b$ cannot be the largest element in the list because $a$ is already larger than $b$. Thus, $b$ is guaranteed to not be the largest.

In either case, we identify an element that is definitely not the largest using exactly $1$ comparison.

Therefore, the minimum number of element comparisons required is $1$.