binary search

Binary search is easy to describe and famously easy to get wrong (off-by-one, infinite loops). The signal is a correct template plus the variants (boundaries, rotated arrays) that come up constantly. Here is the answer.

LIS has an obvious O(n²) DP and a clever O(n log n) solution that surprises people. The signal is the patience-sorting/binary-search approach maintaining 'tails'. Here is both.

This famously-hard problem wants better than the O(m+n) merge: an O(log) binary search on the partition. The signal is binary-searching the split point so the left halves stay below the right halves. Here is the answer.

A row- and column-sorted matrix rewards one observation: start from a corner and kill an entire row or column each step. That turns an O(m*n) scan into O(m+n), and the choice of corner is not arbitrary.

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

A time-based key-value store records 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.