Competitive Programming – A Complete Guide

Competitive Programming is a mental sport which enables you to code a given problem under provided constraints. The purpose of this article is to guide every individual possessing a desire to excel in this sport. This article provides a detailed syllabus for Competitive Programming designed by industry experts to boost the preparation of the readers.

Topic:

Introduction

• What is Competitive Programming and How to Prepare for It?
• Fast I/O: CPP,  Java, Python
• Useful libraries: CPP, Java, Python
• Input/Output Files: Set 1, Set 2
• Tips and Tricks: Set 1, Set 2
• Input Methods: CPP, Java, Python
• Template: CPP
• Language: CPP, Java, Python
• Time Complexity: Analysis 
• Setting up Competitive Programming Environment: Sublime: CPP, Visual Studio: CPP and Python

Basics, Greedy and Bit Manipulation

• Reverse an array (Related Problems: Problem 1, Problem 2)
• Sum of Digits
• Program to Check if a Given String is Palindrome in C, Python (Related Problem)
• Sum of array elements   (Related Problem)
• Maximum and Minimum element of array   (Related Problem)
• Counting frequencies of array elements (Related Problems: Problem 1, Problem 2)
• Float and Precision: CPP, Java, Python
• Prefix sum, 2D Prefix Sum Difference Array | Range update query in O(1): (Related Problems: Problem 1, Problem 2)
• Coordinate Compression: (Related Problem)
• Kadane Algorithm: (Related Problem)
• Activity Selection Problem: (Related Problem)
• Job Sequencing Problem: (Related Problem)
• Sliding Window: (Related Problem)
• Logical Operators: CPP Set 1, Set 2, Java, Python
• Bit Manipulation: Set 1, Set 2, Set 3 (Related Problems: Problem 1, Problem 2, Problem 3)
• Bitset CPP

Number Theory and Combinatorics

• Prime Number (Related Problem)
• Sieve of Eratosthenes (Related Problem)
• Segmented Sieve (Related Problem)
• Find all divisors of a natural number (Related Problem)
• Least prime factor of numbers upto N (Related Problem)
• All prime factors of a number (Related Problem)
• Prime Factorization using Sieve O(log n) for multiple queries
• Sum of all factors of a number (Related Problem)
• Gcd of Two numbers, Lcm of two numbers (Related Problem)
• Linear Diophantine Equations
• Euclidean algorithms (Basic and Extended)
• Euler’s Totient Function (Related Problem)
• Euler’s Totient function for all numbers smaller than or equal to n
• Inclusion Exclusion Principle 
• Pigeon Hole Principle
• Modular Operations
• Modular Inverse: (Related Problem 1, Problem 2)
• Chinese Remainder Theorem: Set 1, Set 2
• Power(x, y) in O( logN )
• Power(x, y) % mod: (Related Problem 1, Problem 2)
• Matrix Exponentiation: (Related Problem)
• Permutation and Combination: Set 1, Set 2, Quiz 1, Quiz 2
• nCr: Set 1, Set 2
• nCr % mod: Set1, Set 2: (Related Problem)
• nCr % mod for multiple queries: (Related Problem)
• Catalan numbers: Applications and Related Problem
• Gaussian Elimination

Searching, Sorting and Basic Data Structures

• Linear Search (Related Problems : Problem 1, Problem 2)
• Binary Search, Unbounded Binary Search (Related Problems : Problem 1, Problem 2, Problem 3)
• Inbuilt sorting O(logN): CPP, Java, Python (Related Problems : Problem 1, Problem 2, Problem 3, Problem 4)
• Merge Sort (Related Problems : Problem 1, Problem 2)
• Quick Sort (Related Problems : Problem)
• Stack: Implementation in CPP, Java, Python (Related Problems : Problem 1, Problem 2, Problem 3)
• Queue: Implementation in CPP, Java, Python (Related Problems : Problem 1, Problem 2 , Problem 3)
• Deque: Implementation in CPP, Java, Python (Related Problems : Problem)
• Priority Queue: Implementation in CPP, Java, Python (Related Problems : Problem 1, Problem 2, Problem 3)

Tree and Graphs

• Tree BFS, Tree DFS (Related Problems : Problem 1, Problem 2, Problem 3)
• Graph BFS, Graph BFS 2, Graph DFS (Related Problems : Problem 1, Problem 2)
• Dijkstra’s Shortest Path Algorithm (Related Problems : Problem 1, Problem 2)
• Bellman – Ford Algorithm (Related Problem)
• Floyd Warshall Algorithm (Related Problem)
• 0-1 BFS, Dial’s Algorithm
• Detect cycle: Directed, Undirected (Related Problems : Problem 1, Problem 2)
• Disjoint set(union-find): Set 1, Set 2, Set 3 (Related Problem)
• Topological Sorting, Kahn’s Algorithm (Related Problem)
• Minimum Spanning Tree: Prim’s Algorithm, Kruskal Algorithm (Related Problem)
• Bipartite or not, M-Coloring (Related Problems : Problem 1, Problem 2, Problem 3)
• Strongly Connected Components: Tarjan, Kosaraju (Related Problems : Problem 1 , Problem 2)
• Euler Path: Undirected, Directed (Related Problem)
• Flow Algorithms: Set 1, Set 2, Dinic’s Algorithm (Related Problems : Problem 1, Problem 2)
• Diameter of Tree
• Centroid Decomposition
• Lowest Common Ancestor

Recursion and Dynamic Programming

• Recursion:  Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7 (Related Problems : Problem 1, Problem 2, Problem 3)
• Backtracking: (Related Problems : Problem 1, Problem 2)
• Dp Introduction: Set 1, Set 2, Set 3, Set 4, Set 5
• Most useful Dynamic Programming questions
• Additional DP Problems : Problem 1, Problem 2, Problem 3, Problem 4
• Dp on Trees: Set 1, Set 2
• Dp on Bit Masking: Set 1, Set 2, Set 3
• Digit Dp

String Algorithms

• Suffix Tree: Set 1, Set 2
• Z Algorithm
• KMP Algorithm, Rabin-Karp Algorithm (Related Problem)
• Manacher’s Algorithm: Set 1, Set 2, Set 3, Set 4
• Suffix Automation: Set 1, Set 2

Geometry and Game Theory

• Closest Pair of Points
• How to check if two given line segments intersect? (Related Problem)
• How to check if a given point lies inside or outside a polygon?
• Convex Hull: Set 1, Set 2 (Related Problem)
• Given n line segments, find if any two segments intersect
• Check whether a given point lies inside a triangle or not
• How to check if given four points form a square: (Related Problem)
• Combinatorial Game Theory: Set 1 , Set 2, Set 3, Set 4
• Minimax Algorithm in Game Theory: Set 1, Set 2, Set 3, Set 4, Set 5
• Variation in Nim Game
• Find the winner in nim-game
• Optimal Strategy for a Game

Advance Data Structures

• Trie: Set 1, Set 2, Set 3, (Related Problems: Problem 1, Problem 2, Problem 3, Problem 4, Problem 5)
• Fenwick Tree: Set 1, Set 2, Set 3, Set 4, (Related Problem)
• Segment Tree: Set 1, Set 2, Set 3 (Related Problem)
• Sparse Table: Set 1, Set 2
• Sqrt Decomposition: Set 1, Set 2
• Heavy Light Decomposition: Set 1, Set 2
• Meet in the Middle
• MO’s Algorithm, Problem
• Policy based Data Structure

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