📐 Data Structures & Algorithms
A reference guide for essential DSA concepts. Dummy content to get started.
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Data Structures
Arrays
- Contiguous memory, O(1) random access
- Insert/delete at end: O(1) amortized
- Insert/delete at arbitrary position: O(n)
Linked Lists
- Singly Linked: each node has data + next pointer
- Doubly Linked: each node has data + next + prev pointers
- Operations: search O(n), insert at head O(1), delete O(n)
Stacks
- LIFO (Last In, First Out)
- Operations: push, pop, peek — all O(1)
- Use cases: undo/redo, expression evaluation, DFS
Queues
- FIFO (First In, First Out)
- Operations: enqueue, dequeue, front — all O(1)
- Variants: circular queue, deque, priority queue
Hash Tables
- Key-value storage, average O(1) operations
- Collision resolution: chaining, open addressing
- Load factor determines resizing threshold
Trees
| Type |
Description |
| Binary Tree |
Each node has ≤2 children |
| BST |
Left < root < right; search O(log n) avg |
| AVL Tree |
Self-balancing BST (height diff ≤1) |
| Red-Black Tree |
Self-balancing with color constraints |
| Heap |
Complete binary tree, min/max at root |
| Trie |
Prefix tree for strings |
Graphs
- Representation: adjacency matrix (O(V²) space), adjacency list (O(V+E) space)
- Traversal: BFS (queue, level-order), DFS (stack/recursion, depth-order)
- Applications: shortest path, connectivity, topological sort
Algorithms
Sorting
| Algorithm |
Best |
Average |
Worst |
Space |
| Quick Sort |
O(n log n) |
O(n log n) |
O(n²) |
O(log n) |
| Merge Sort |
O(n log n) |
O(n log n) |
O(n log n) |
O(n) |
| Heap Sort |
O(n log n) |
O(n log n) |
O(n log n) |
O(1) |
| Bubble Sort |
O(n) |
O(n²) |
O(n²) |
O(1) |
| Insertion Sort |
O(n) |
O(n²) |
O(n²) |
O(1) |
Searching
- Linear Search: O(n)
- Binary Search: O(log n) — requires sorted array
Graph Algorithms
- BFS / DFS — O(V+E) traversal
- Dijkstra's — shortest path, O((V+E) log V)
- Bellman-Ford — handles negative edges, O(VE)
- Floyd-Warshall — all-pairs shortest path, O(V³)
- Kruskal's / Prim's — MST, O(E log V)
- Topological Sort — DAG ordering, O(V+E)
Dynamic Programming
- Optimal substructure + overlapping subproblems
- Top-down (memoization) vs bottom-up (tabulation)
- Classic problems: Fibonacci, Knapsack, LCS, LIS, Edit Distance
String Algorithms
- KMP — pattern matching, O(n+m)
- Rabin-Karp — rolling hash, average O(n+m)
- Z-Algorithm — pattern matching, O(n)
- Manacher's — longest palindromic substring, O(n)
Complexity Reference
| Notation |
Name |
Description |
| O(1) |
Constant |
Direct access |
| O(log n) |
Logarithmic |
Binary search, balanced trees |
| O(n) |
Linear |
Single pass |
| O(n log n) |
Linearithmic |
Efficient sorting |
| O(n²) |
Quadratic |
Nested loops |
| O(2ⁿ) |
Exponential |
Recursive subsets |
| O(n!) |
Factorial |
Permutations |
Practice Sheets
- LeetCode — Solved LeetCode problems
- Codeforces — Codeforces problem archive by rating
- CSES — CSES Problem Set (300+ problems)
- CP-31 — TLE Eliminators CP-31 sheet (372 problems)
- NeetCode — NeetCode 150 roadmap