Big-O Reference Chart
Big-O notation reference for common algorithms and data structures with time and space complexity.
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Complexity Scale (Best to Worst)
O(1) (Constant)
O(log n) (Logarithmic)
O(n) (Linear)
O(n log n) (Linearithmic)
O(n^2) (Quadratic)
O(2^n) (Exponential)
| Algorithm | Best | Average | Worst | Space |
|---|---|---|---|---|
| Bubble Sort | O(n) | O(n^2) | O(n^2) | O(1) |
| Selection Sort | O(n^2) | O(n^2) | O(n^2) | O(1) |
| Insertion Sort | O(n) | O(n^2) | O(n^2) | O(1) |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) |
| Quick Sort | O(n log n) | O(n log n) | O(n^2) | O(log n) |
| Heap Sort | O(n log n) | O(n log n) | O(n log n) | O(1) |
| Counting Sort | O(n+k) | O(n+k) | O(n+k) | O(k) |
| Radix Sort | O(nk) | O(nk) | O(nk) | O(n+k) |
| Linear Search | O(1) | O(n) | O(n) | O(1) |
| Binary Search | O(1) | O(log n) | O(log n) | O(1) |
| Array Access | O(1) | O(1) | O(1) | O(n) |
| Array Insert | O(1) | O(n) | O(n) | O(n) |
| Linked List Access | O(1) | O(n) | O(n) | O(n) |
| Linked List Insert | O(1) | O(1) | O(1) | O(n) |
| Hash Table Search | O(1) | O(1) | O(n) | O(n) |
| BST Search | O(log n) | O(log n) | O(n) | O(n) |
| BFS | O(V+E) | O(V+E) | O(V+E) | O(V) |
| DFS | O(V+E) | O(V+E) | O(V+E) | O(V) |
| Dijkstra's | O(E log V) | O(E log V) | O(E log V) | O(V) |
About Big-O Notation
Big-O notation describes the upper bound of an algorithm's growth rate. It helps compare algorithms by their efficiency as input size increases.
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