Algorithm list for Contest.txt

Mathematics:

(a)Number Theory

    Prime Number Generation  (Sieve, Segmented Sieve)
    Euler Totient Theorem
    Fermat’s Theorem
    HCF & LCM (Euclid)
    Linear Diophantine Equations (Extended Euclid)
    Modulus Arithmetic (addition,multiplication,subtraction,modular Inverse)
    Cycle Finding (Floyd Algo and Brent Algo)
    Integer Factorization (Trial Division , Pollard Rho method)
    Lucas Theorem  (Simple & Advance)
    Chinese Remainder Theorem
    Wilson Theorem
    Miller - Rabin Primality Testing
    Perfect Numbers
    Goldbach Conjecture


(b)Probability

    Basic Probability and Conditional Probability
    Random Variables
    Probability Generating Functions
    Expectation
    Probability Distribution [Binomial, Poisson, Normal,Bernoulli]


(c)Counting

    Pigeonhole principle
    Inclusion Exclusion
    Special Numbers  [Stirling,Fibonacci,Catalan, Eulerian, Harmonic, Bernoulli]
    Polya Counting
    Burnside lemma


(d)Permutation Cycles

(e)Linear Algebra

    Addition And Subtraction Of Matrices
    Multiplication ( Strassen's algorithm ), Logarithmic exponentiation
    Matrix Transformations [ Transpose, Rotation Of Matrix, Representing Linear Transformations Using Matrix ]
    Determinant , Rank and Inverse Of Matrix [ Gaussian Elimination , Gauss Jordan Elimination]
    Solving System Of Linear Equations
    Matrix Exponentiation To Solve Recurrences
    Eigenvalues And Eigen vector
    Roots of a polynomial [ Prime factorization of a polynomial, Integer roots of a polynomial]
    Lagrange Interpolation


(e)Game Theory

    Basic Concepts & Nim Game [Grundy Theorem , Grundy Number]
    Hackenbush


(f)Group Theory

    Burnside Lemma
    Polya's Theorem

  
Graphs:

(a)Graph Representation

    Adjacency Matrix
    Adjacency List
    Incidence Matrix
    Edge List


(b)Graph Types

    Directed
    Undirected
    Weighted
    Unweighted
    Planar
    Hamilton
    Euler
    Special Graphs


(c)DFS & It’s Application

    Cycle Detection
    Articulation Points
    Bridges
    Strongly Connected Component
    Connected Component
    Path Finding
    Solving Maze
    Biconnectivity in Graph
    Topological Sorting
    Bipartite Checking
    Planarity Testing
    Flood-fill algorithm


(d)BFS & It’s Application

    Shortest Path (No. Of Edges)
    Bipartite Checking
    Connected Components


(d)Minimum Spanning Tree

    Prim’s Algorithm
    Kruskal Algorithm


(d)Single Source Shortest-Path

    Dijkstra
    Bellman Ford


(e)All pair Shortest Path

    Floyd Warshall’s Algorithm


(f)Euler Tour

(g)Flow

    Ford-Fulkerson [PFS,DFS,BFS]
    Dinic's Algorithm
    Min Cost - Max Flow  [Successive Shortest Path Algo,Cycle Cancelling Algorithm]
    Max Weighted BPM  [Kuhn Munkres algorithm/Hungarian Method]
    Stoer Wagner Min-Cut Algo
    Hop-Kraft BPM
    Edmond Blossom Shrinking Algorithm


(h)Other Important Topics On Graphs

    2-SAT,
    LCA
    Maximum Cardinality Matching
    Application Flow
    Min Path Cover Over Dag
    Independent Edge Disjoint Path
    Minimum Vertex Cover
    Maximum Independent Set


Data Structures:

    Arrays
    Linked List
    Trees (Binary Tree And Binary Search Tree)
    Stacks
    Queues
    Heap
    Hash Tables
    Disjoint-Set Data Structures
    Trie
    Segment Tree
    Binary Index Tree
    Treap


Searching And Sorting:

    Linear Search
    BInary Search
    Ternary Search
    Selection Sort
    Bubble Sort
    Insertion Sort
    Merge Sort
    Quick Sort
    Quick Select
    Heap Sort
    Radix Sort
    Counting Sort


Greedy:
Classical Problems of Greedy & Concept
example : Fractional Knapsack


Dynamic Programming Classical Problems

    Edit Distance
    Egg Dropping Puzzle
    Integer Knapsack
    Largest Independent Set
    Longest Biotonic Subsequence
    Longest Common Subsequence
    Longest Common Substring
    Longest Increasing Subsequence
    Longest Palindromic Subsequence
    Longest Palindromic Substring
    Longest Substring Without Repeating Character
    Matrix Chain Multiplication
    Max Size Square Submatrix With One
    Maximum Length Chain Pairs
    Maximum Sum Increasing Subsequence
    Optimal Binary Search Tree
    Palindrome Partition Problem
    Set Partition Problem
    Subset Sum
    Word Wrap Problem


Dynamic Programming  Advanced Techniques

    DP + Tree
    DP + Bit Masking
    DP + Binary Search
    DP + Graph
    DP + Matrix Exponentiation
    DP + Probability Space
    DP + Crack Recurrence


Divide & Conquer
Classical Problems & Concepts

    Merge Sort
    Closest Pair Points


Other Algorithm Design Techniques :

    BackTracking
    Man In Middle
    Newton-Raphson to reach the fixed point
    Brute Force
    Constructive Algo
    Sliding Window
    Pancake Sorting