Valid Perfect Square - Binary Search

The squares $1^2, 2^2, 3^2, ...$ form an increasing sequence. This means you can use binary search.

Start with $left = 1$ and $right = num$. Compute $mid$ and check $mid^2$. If $mid^2 = num$, you found it. If $mid^2 < num$, search the right half. If $mid^2 > num$, search the left half.

Watch out for overflow when computing $mid^2$. If $mid$ is large, the product might exceed integer limits.