SteveDengZishi/ACM_UVA_algorithmic_problem_solving

This repository contains useful templates for competitive programming that can be used in ACM and UVa problem solving.

Using C++ 5.3.0 with -std=c++11

Some templates are written by myself and some are inspired by other talented authors and then modified to either general or specific usage.

Contents Table:

Template:

    General template for c++ competitive problem solving

Special Data Structures:

    Union-Find or Disjointed set implementation
    Fenwick Tree(Binary Indexed Tree) implementation
    Segment Tree implementation
    //Suffix Tree

Techniques:

    Longest Increasing Subseqence(LIS)
    Maximum Sum Subarray(Kadane's Algorithm)
    Dynamic Programming + Memoization

Graph Algorithms:
    
    UNWEIGHTED SHORTEST PATH:
    Breath First Search(BFS) O(V+E)
    Depth First Search(DFS) O(V+E)

    WEIGHTED SHORTEST PATH:
    Dijkstra's algorithm --- single-source shortest path problem. O(ElogV) E times logV using extract min from heap
    Bellman–Ford algorithm --- single-source problem if edge weights may be negative. O(VE) O(V^2) on sparse O(V^3) on dense.
    Floyd–Warshall algorithm --- all pairs shortest paths. O(V^3) dp three for loop ijk
    //Johnson's algorithm --- all pairs shortest paths, and may be faster than Floyd–Warshall on sparse graphs.
    SPFA(Shortest Path Faster Algorithm) --- Improve performance of Bellman-Ford
    
    UNWEIGHTED ORDERING:
    Topological Sort(dfs + stack)

    MINIMUM SPANNING TREE:
    Kruskal's algorithm
    Prim's algorithm

    MAXFLOW MIN-CUT:
    Ford-Fullkerson algorithm

    ARTICULATION & BRIDGES:
    Tarjan's Algorithm

String Algorithms:
    
    Violent string matching O(TP)
    Knuth-Morris-Pratt(KMP) O(T+P)

Geometry:
    
    Graham scanning(Convex Hull) O(n^2 log n)

SteveDengZishi / ACM_UVA_algorithmic_problem_solving

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