Lecture 4: Fundamental Number Theory and Mathematical Concepts for Competitive Programming

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Lecture 4 delves into the fundamentals of number theory and key mathematical concepts essential for competitive programming. It covers topics like prime numbers, divisibility rules, modular arithmetic, and gcd (greatest common divisor), providing a strong foundation for solving algorithmic problems efficiently. This lecture equips learners with the mathematical tools to approach challenges with confidence.

Video Timestamps:-
00:00:00 Introduction
00:02:20 What is Number Theory?
00:03:00 Today’s Agenda
00:04:55 Prime Numbers
00:18:00 Finding factors of a Number
00:29:05 Checking Prime Number in Efficient Time
00:31:45 Sieve of Eratosthenes
00:53:00 Time Complexity of Sieve of Eratosthenes
00:56:00 Why Sieve is Better?
01:01:20 Problem A - Primes
01:10:20 Problem B - Prefix Sum Primes
01:23:25 Problem C - Factorise N+M
01:30:30 Problem D - Prime Deletion
01:38:30 Problem E - Prime Substraction
01:45:35 Modular Arithmetic
01:54:54 Binary Exponentiation
02:11:55 Modular Exponentiation
02:20:35 Problem F - Modular Exponentiation
02:36:35 GCD - Greatest Common Divisor
02:43:00 Euclidean Algorithm
02:56:00 LCM - Lowest Common Multiple
03:01:50 Problem G - LCM Problem
03:11:05 Problem H - GCD vs LCM
03:17:30 Problem I - Madoka and Strange Thoughts
03:26:45 Finding Factorial of a Number
03:30:20 Finding value of nCr
03:40:40 Problem J - Password
03:48:50 Problem K - Required Remainder
03:58:20 Conclusion

Resources:

Sieve of Eratosthenes: https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html
Euclidean algorithm: https://cp-algorithms.com/algebra/euclid-algorithm.html
Time Complexity of Euclid’s Algorithm: https://www.baeldung.com/cs/euclid-time-complexity
nCr: https://cp-algorithms.com/combinatorics/binomial-coefficients.html
Binary Exponentiation: https://cp-algorithms.com/algebra/binary-exp.html

Problems Solved:

B. Primes: https://codeforces.com/problemset/gymProblem/102267/B
A. Prefix Sum Primes: https://codeforces.com/problemset/problem/1149/A
A. Factorise N+M: https://codeforces.com/problemset/problem/1740/A
A. Prime Deletion: https://codeforces.com/problemset/problem/1861/A
A. Prime Subtraction: https://codeforces.com/problemset/problem/1238/A
A. Modular Exponentiation: https://codeforces.com/problemset/problem/913/A
A. LCM Problem: https://codeforces.com/problemset/problem/1389/A
A. Required Remainder: https://codeforces.com/problemset/problem/1374/A
A. GCD vs LCM: https://codeforces.com/problemset/problem/1665/A
A. Password: https://codeforces.com/problemset/problem/1743/A
A. Madoka and Strange Thoughts: https://codeforces.com/problemset/problem/1717/A

Lecture 4 : Understanding Number Theory and Maths Concepts | Competitive Programming

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