library

Some useful algorithms for competitive programming

Complexity Table

Data Structure Storage Build Point Update Range Update Point Query Range Query
Segment Tree O(n) O(n) O(log n) O(log n) O(log n) O(log n)
Fenwick Tree O(n) O(n) O(log n) O(log n) O(log n) O(log n)
Sparse Table O(n log n) O(n log n) - - O(1) O(1)
Segment Tree (2D) O(n2) O(n) O(log2 n) O(log2 n) O(log2 n) O(log2 n)
Fenwick Tree (2D) O(n2) O(n) O(log2 n) - O(log2 n) O(log2 n)
Quadtree O(n2) O(n) O(log n) O(log n) O(log n) O(n)