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

Use "DSA20" To Get Extra 20% Off On All Decode Batches Want to Get Enrolled in Decode Batches? Enroll Now-https://pwskills.com/category/programming-courses/?utm_source=organic&utm_medium=social_media&utm_campaign=winter_sale 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 #NumberTheory #CompetitiveProgramming #Mathematics #GCD #ModularArithmetic #PrimeNumbers #Algorithms