🎯 Pattern Playbook: recognize → apply

If the problem says…	Think…
Sorted array, find pair/triplet	Two pointers
Contiguous subarray/substring with a condition	Sliding window (variable) / prefix sum + hashmap
Subarray sum = K (negatives allowed)	Prefix sum + hashmap
”Next greater/smaller”, histogram, stock span	Monotonic stack
Sliding-window max/min	Monotonic deque
Sorted / monotonic answer space, “minimize the max”	Binary search (on the answer)
Top/Kth largest, merge K sorted, streaming median	Heap(s)
All combinations/permutations/subsets	Backtracking
Shortest path, unweighted	BFS
Shortest path, weighted non-negative	Dijkstra
Negative weights	Bellman-Ford
Dependencies / ordering	Topological sort
Connectivity, grouping, cycle in undirected graph	Union-Find (DSU)
Prefix/word lookup, autocomplete	Trie
Overlapping intervals	Sort by start + merge / sweep line / min-heap of ends
Optimal value over choices with overlapping subproblems	DP (define state → transition → base → order)
“Count ways”	DP / combinatorics
Range queries with updates	Segment tree / Fenwick tree
Linked list cycle / middle	Fast & slow pointers
XOR tricks, subsets as masks	Bit manipulation
LRU/LFU, design a data structure	HashMap + doubly linked list / multiple maps

DP framework

State: what minimal info defines a subproblem? dp[i], dp[i][j], dp[mask]
Transition: how does the state build from smaller states?
Base cases
Order (top-down memo first, then convert to bottom-up, then space-optimize)
Answer location

Restate the problem and confirm the I/O, constraints, and edge cases (empty, duplicates, negatives, overflow)
Walk through 1–2 examples by hand
State the brute force + its complexity
Optimize: name the pattern and why it fits
Code cleanly (good names, helper methods)
Dry-run the code on an example; test edge cases
State time/space complexity; discuss follow-ups