DSA Patterns

Hashing trades memory for time — O(n²) lookup becomes O(n).

Sorted input? Converge from both ends and eliminate halves.

Grow right until invalid, shrink left until valid — record the best.

When order reverses or pairs must match — think stack.

If the answer space is monotonic, you can binary search the answer.

Dummy nodes kill edge cases; fast & slow pointers find middles and cycles.

Almost every tree problem is DFS returning information upward, or BFS by levels.

Prefix problems = a tree where every edge is a character.

K-th anything, streaming medians, always-cheapest-first — reach for a heap.

Choose → explore → un-choose. Draw the decision tree first.

Islands = flood fill. Ordering = topological sort. Shortest path = BFS / Dijkstra.

DP = recursion + memory. Define state, then the decision at each state.

Two sequences or a grid? Your state needs two coordinates.

Greedy works when a local best choice never blocks the global best.

Interleave everything. The exam never tells you the pattern name.