Algorithm Patterns

The reusable moves behind interview problems — recognize each pattern, run it, and prove why it works.

Scanning & windows

Linear passes that touch each element O(1) times: pointers, windows, prefix sums, and hash lookups.

Exploit order: halve sorted spaces, keep monotonic stacks, sweep intervals, and track top-k with heaps.

Structural moves on linked nodes, prefix trees, and binary representations.

Visit every node with intent: layer order, depth order, parity, and dependency order.

Merge components with union-find, span them cheaply, and settle shortest distances greedily.

Commit greedily with proof, backtrack on dead ends, or memoize overlapping subproblems.

Choose the invariant and data movement that fit each common problem shape.