Off-by-One Errors

Mistake 1: Using high = arr.length - 1 for lower bound.

Lower bound can return arr.length if all elements are smaller. Initialize high = arr.length.

Mistake 2: Using while low <= high for lower bound.

Lower bound converges when low == high. Using <= causes extra iterations or wrong answers.

Mistake 3: Returning mid instead of low after the loop.

For lower bound, the answer is low (which equals high) after the loop ends.

Debugging tip: Trace through with a $2$-element array like $[1, 3]$ searching for $0$, $1$, $2$, $3$, and $4$. Cover all edge cases.