Patterns

Longest/shortest/max/min contiguous subarray or substring

Grow right, shrink left while the window is invalid.

Sorted array, find a pair/triplet hitting a target

Converge left/right pointers.

Range sums, or subarray sum equals K (with negatives)

Precompute cumulative sums; range = P[j]-P[i]; pair with a hashmap.

Values in 1..n; find duplicate/missing in O(1) space

The array is its own hash table.

Merge/insert overlapping intervals, meeting rooms

Sort by start, merge when curr.start <= prev.end.

Sorted array, find a boundary, or O(log n) required

Find the monotonic yes/no predicate; while lo <= hi.

Search in a rotated sorted array

One half is always sorted; decide which to keep.

Matching/balance/nesting, undo last

Push openers, pop and verify on closers.

Next greater/smaller, nearest larger to the right

Keep an increasing/decreasing stack; each pop resolves an answer.

Linked list cycle/middle/nth-from-end

Two pointers at different speeds (tortoise and hare).

Top K / K largest / K closest / K most frequent

Keep a size-K heap; push/pop is O(log K).

Level order, min depth, width per level

Process one whole level at a time with a queue.

Root-to-leaf path, subtree logic, validation

Recurse; pass bounds/state down.

Islands/regions in a grid, shortest steps

Flood-fill with a visited set; BFS for shortest.

Prerequisites, ordering, can-you-finish, dependencies

Indegree + queue (Kahn); leftovers mean a cycle.

Connected groups, friend circles, merge accounts

Union elements, count distinct roots; path compression + rank.

Generate all subsets/permutations/combinations

Choose, recurse, un-choose; prune early.

Number of ways / min cost / max value with overlapping choices

Define state, transition, base case.

Two strings: edit distance, LCS, grid paths

Grid of subproblems indexed by (i, j).

Palindromic substrings or longest palindromic subsequence

Expand around each center, or fill a 2-D table.

Seen-before, count frequencies, group by key, deduplicate

Trade space for O(1) lookups.