Covering algorithms used in combinatorial game theory puzzles

What you will learn

Learn about concept of combinatorial game theory

Common algorithms used in combinatorial game theory problems

Practice algorithm questions from popular online coding competitions

Thorough understanding on the correctness and efficiency of the algorithms

Look at algorithms from a mathematical point of view

Implement these algorithms yourself or with a bit of guidance


This is a series of courses on popular algorithms used especially in the field of competitive programming!

Competitive programming is a mental sport that tests students on a variety of logical or mathematical problems, and the use of algorithms is essential in improving the efficiency of your solution.

The aim of competitive programming is to write source code of computer programs that are able to solve given problems. Typical such tasks belong to one of the following categories: combinatorics, number theory, graph theory, algorithmic game theory, computational geometry, string analysis, and data structures.

This course focuses not only on the implementation of algorithms but also on the mathematics behind these algorithms since they are requisite in understanding the correctness and efficiency of the algorithms. Specifically, rigid proofs for algorithms will be covered in this series of lectures.

This is the first course in the series Algorithms in Competitive Programming: Maths Puzzles II. In this course, we will be learning about combinatorial game theory, a rather niche topic in competitive programming. However, it is(arguably) one of the most interesting topics and there is more mathematical logic behind these combinatorial puzzles than you would have imagined.

If you find this course intriguing or you want to learn more about competitive programming algorithms, please look forward to future addition to the series!

A typical course structure is as follows:

– Problem description

– A naive approach

– Introducing the algorithm

– Mathematical proof of the correctness and efficiency of the algorithm

– A sample problem

– Short quiz

– Hands-on practice





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Revision Quiz: Time Complexity

Nim’s Game

Combinatorial Game Theory

Representation of an Nim’s Game

Nim’s Game: Winning Strategy

Nim’s Game: Code Implementation

Nim’s Game

Classical Nim’s Game

Nim’s Game: Some Variants

Example 1

Example 1: Code Implementation

Example 1

Example 2

Example 2: Code Implementation

Example 2

More Advanced Combinatorial Games

Example(Sourced From USACO Gold Category)

Code Implementation

Example(Sourced From USACO Gold Category)