binary search

Binary search is simple to explain and notoriously easy to botch (off-by-one, infinite loops). Interviewers look for a correct template plus the variants (boundaries, rotated arrays) that show up constantly. The answer follows.

LIS has an obvious O(n²) DP and a clever O(n log n) solution that catches people off guard. Interviewers look for the patience-sorting/binary-search approach that maintains 'tails'. Both appear below.

This notoriously hard problem demands better than the O(m+n) merge: an O(log) binary search on the partition. Interviewers look for binary-searching the split point so the left halves stay below the right halves. The answer follows.

A row- and column-sorted matrix rewards a single insight: begin at a corner and drop a whole row or column each step. That converts an O(m*n) scan into O(m+n), and which corner you pick is not arbitrary.

Binary search on the answer cracks minimize-the-maximum and capacity problems by guessing the result and testing feasibility with a monotone predicate. The signal is spotting monotonicity and writing a clean feasibility function. Here is the answer.

A time-based key-value store logs versioned writes and answers 'what was the value at time t' via binary search over per-key timestamps. The signal is the append-only design and the floor (largest timestamp <= t) lookup. Here is the answer.