Cheatsheet

The whole map on one page: which family a problem belongs to, and which signal points at which pattern.

7 families

Array Sweeps

You move indices along a line.

Binary Search

Sorted input, or an O(log n) requirement.

Linear Helpers

Process a sequence with one helper structure.

Heap

Keep only the important few.

Trees & Graphs

Traverse a structure.

Recursion Family

Explore possibilities or optimize.

Hashmap (sidekick)

Always-on tool to turn O(n^2) into O(n).

Signal → pattern (21)

Interview signals mapped to the pattern that solves them, grouped by family
If you see this signal	Reach for
Array Sweeps
Longest/shortest/max/min contiguous subarray or substring	Sliding Window Grow right, shrink left while the window is invalid.
Sorted array, find a pair/triplet hitting a target	Two Pointers Converge left/right pointers.
Range sums, or subarray sum equals K (with negatives)	Prefix Sum Precompute cumulative sums; range = P[j]-P[i]; pair with a hashmap.
Values in 1..n; find duplicate/missing in O(1) space	Cyclic Sort / Index-as-Hash The array is its own hash table.
Merge/insert overlapping intervals, meeting rooms	Intervals Sort by start, merge when curr.start <= prev.end.
Binary Search
Sorted array, find a boundary, or O(log n) required	Binary Search Find the monotonic yes/no predicate; while lo <= hi.
Search in a rotated sorted array	Rotated Binary Search One half is always sorted; decide which to keep.
Linear Helpers
Matching/balance/nesting, undo last	Stack Push openers, pop and verify on closers.
Next greater/smaller, nearest larger to the right	Monotonic Stack Keep an increasing/decreasing stack; each pop resolves an answer.
Linked list cycle/middle/nth-from-end	Fast & Slow Pointers Two pointers at different speeds (tortoise and hare).
Heap
Top K / K largest / K closest / K most frequent	Heap / Priority Queue Keep a size-K heap; push/pop is O(log K).
Trees & Graphs
Level order, min depth, width per level	Tree BFS Process one whole level at a time with a queue.
Root-to-leaf path, subtree logic, validation	Tree DFS Recurse; pass bounds/state down.
Islands/regions in a grid, shortest steps	Graph BFS/DFS Flood-fill with a visited set; BFS for shortest.
Prerequisites, ordering, can-you-finish, dependencies	Topological Sort Indegree + queue (Kahn); leftovers mean a cycle.
Connected groups, friend circles, merge accounts	Union-Find Union elements, count distinct roots; path compression + rank.
Recursion Family
Generate all subsets/permutations/combinations	Backtracking Choose, recurse, un-choose; prune early.
Number of ways / min cost / max value with overlapping choices	1-D Dynamic Programming Define state, transition, base case.
Two strings: edit distance, LCS, grid paths	2-D Dynamic Programming Grid of subproblems indexed by (i, j).
Palindromic substrings or longest palindromic subsequence	Palindrome DP Expand around each center, or fill a 2-D table.
Hashmap (sidekick)
Seen-before, count frequencies, group by key, deduplicate	Hashmap / Set Trade space for O(1) lookups.