Arrays & Strings
Two Pointers
Use it when you see: a sorted array, “find a pair/triplet summing to target,” “remove duplicates in place,” or “is it a palindrome.”
The 17 core patterns — and how to spot them
Map the wording of the question to a pattern. The “Use it when you see” phrases are the fastest way to narrow down your approach in the first 60 seconds.
Arrays & Strings
Sliding Window
Use it when you see: “longest/shortest contiguous substring/subarray,” “max sum of size k,” or “at most K distinct.”
Linked Lists
Fast & Slow Pointers
Use it when you see: “detect a cycle in a linked list,” “find the middle node,” or “happy number.”
Arrays & Strings
Merge Intervals
Use it when you see: “overlapping intervals,” “merge,” “meeting rooms,” or “insert an interval.”
Arrays & Strings
Cyclic Sort
Use it when you see: an array of numbers in the range 1..n, “find the missing/duplicate number,” or “in-place, O(1) space.”
Linked Lists
In-place Reversal
Use it when you see: “reverse a linked list,” “reverse a sublist,” or “reverse every k nodes.”
Trees & Graphs
BFS
Use it when you see: “level order traversal,” “shortest path in an unweighted graph,” or “minimum number of steps.”
Trees & Graphs
DFS
Use it when you see: “all paths,” “connected components,” “does a path exist,” or “flood fill.”
Heaps & Top-K
Two Heaps
Use it when you see: “median of a data stream,” “find the median,” or “balance two halves.”
DP & Backtracking
Subsets / Backtracking
Use it when you see: “all combinations/permutations/subsets,” “generate all,” “N-Queens,” or “Sudoku.”
Search & Sort
Modified Binary Search
Use it when you see: a sorted (or rotated sorted) array, “find element/boundary,” or a required O(log n).
Heaps & Top-K
Top K Elements
Use it when you see: “K largest/smallest/most frequent,” or “the Kth element.”
Heaps & Top-K
K-way Merge
Use it when you see: “merge K sorted lists/arrays,” or “smallest range covering K lists.”
Trees & Graphs
Topological Sort
Use it when you see: “course schedule,” “build order,” “dependencies,” or a DAG.
DP & Backtracking
Dynamic Programming
Use it when you see: “count the ways,” “min/max cost,” “can you reach,” or “longest/shortest with choices.”
DP & Backtracking
Greedy
Use it when you see: “maximize/minimize” with a single forward pass, “jump game,” or interval scheduling.
Trees & Graphs
Union-Find (DSU)
Use it when you see: “number of connected components/islands,” “are two nodes connected,” or “grouping.”
No pattern matches that search. Try a phrase from the problem, like “sorted array” or “all permutations.”
Big-O cheat sheet — data structures
Average-case time complexity of the common operations. Reach for the hash map by default; know where the others win.
| Data structure | Access | Search | Insert | Delete | Space |
|---|---|---|---|---|---|
| Array | O(1) | O(n) | O(n) | O(n) | O(n) |
| Dynamic array | O(1) | O(n) | O(1)* | O(n) | O(n) |
| Hash table / map | — | O(1) | O(1) | O(1) | O(n) |
| Stack / Queue | O(n) | O(n) | O(1) | O(1) | O(n) |
| Linked list (singly) | O(n) | O(n) | O(1) | O(1) | O(n) |
| Balanced BST | O(log n) | O(log n) | O(log n) | O(log n) | O(n) |
| Heap / Priority queue | — | O(n) | O(log n) | O(log n) | O(n) |
| Trie | — | O(L) | O(L) | O(L) | O(A·N) |
* amortized · L = key length · A = alphabet size · worst-case for hash table and BST is O(n).
Big-O cheat sheet — algorithms
Know these cold — interviewers expect you to state the complexity of what you write.
| Algorithm | Time | Space | Note |
|---|---|---|---|
| Binary search | O(log n) | O(1) | Array must be sorted |
| Merge / Heap sort | O(n log n) | O(n)/O(1) | Guaranteed n log n |
| Quicksort (avg) | O(n log n) | O(log n) | Worst case O(n²) |
| BFS / DFS | O(V+E) | O(V) | Graph traversal |
| Dijkstra (heap) | O((V+E) log V) | O(V) | Non-negative weights |
| Topological sort | O(V+E) | O(V) | DAG only |
| Subsets / Permutations | O(2^n)/O(n!) | O(n) | Exponential by nature |
FAQ
How do I recognize which pattern a problem needs?
Read for trigger phrases. “Sorted array” + “find a pair” → Two Pointers. “Longest contiguous substring” → Sliding Window. “Numbers 1 to n” → Cyclic Sort. “All combinations” → Backtracking. “Course schedule / dependencies” → Topological Sort. The cards above list these phrases per pattern — that recognition step is usually the whole game.
What is the time complexity of a hash table lookup?
O(1) on average, O(n) worst case under heavy collisions. Insert and delete are also O(1) average — which is why a hash map is the default for membership checks and frequency counts.
How many patterns do I actually need to know?
These 17 cover the large majority of questions asked at most companies. Master the recognition triggers and one clean template per pattern, and you can decompose almost any new problem into something you’ve seen.
Is this cheat sheet free to use and share?
Yes — completely free, no signup, works on any device. Bookmark it or link to it. It’s published by CoPilot Interview as a study reference.
Going from “I know the pattern” to “I can do it live”
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