Competitive programming stuffs

Data structures and algorithms for competitive programming.

Note: This is a publish-only repository and all pull requests are ignored.

Data Structures

1. • Fenwick tree
2. • Fenwick tree 2D
3. • Disjoint set union
4. • DSU w/ rollback
5. • Minimum queue
6. • Segment tree
7. • Segment tree w/ lazy propagation
8. • Persistent segment tree
9. • Sparse table
10. • Ordered set
11. • Treap
12. • Implicit Treap
13. • Merge sort tree

Graph

1. • Dijkstra
2. • Bellman-Ford
3. • Floyd-Warshall
4. • Kruskal
5. • Boruvka
6. • Binary lifting
7. • Eulerian path
8. • Topological sort
9. • Centroid decomposition
10. • Heavy-light decomposition
11. • Edmonds Karp
12. • Dinic's algorithm
13. • Kosaraju
14. • 2-SAT
15. • De Bruijn sequence
16. • Kuhn's algorithm

Dynamic Programming

1. • Longest common subsequence
2. • Longest palindromic subsequence
3. • Longest increasing subsequence - naive O(N^2)
4. • Longest increasing subsequence - fenwick tree O(NlogN)
5. • Longest increasing subsequence - dp & bns O(NlogN)
6. • Travelling salesman problem O(N^2*2^N)

Math

1. • Discrete logarithm
2. • Discrete root
3. • Extended GCD
4. • Linear sieve for divisors count
5. • Linear sieve for divisors sum
6. • Linear sieve for Euler's totient function
7. • Linear Eratosthenes sieve
8. • Least prime factor
9. • Matrix exponentiation
10. • Euler's totient function
11. • Pollard's Rho 128 bit
12. • Pollard's Rho
13. • Primitive root
14. • Rabin–Miller primality test
15. • Segmented sieve
16. • Modular multiplication 64 bit in O(1)
17. • Ternary search
18. • Binomial coefficient w/ Lucas Theorem
19. • Gaussian elimination
20. • Gaussian elimination XOR

String

1. • Longest palindromic substring O(N^2)
2. • Hashing
3. • Hashing w/ update
4. • Hashing 2D
5. • Rabin-Karp
6. • Prefix function
7. • Prefix automaton
8. • Suffix automaton
9. • Z function
10. • KMP
11. • Trie
12. • Lyndon factorization (Duval algorithm)
13. • Suffix array
14. • Longest Common Prefix (Kasai's algorithm)

Others

1. • Mo's algorithm
2. • First element greater than element i from left/right
3. • Check ancestor in O(1)