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Important Math Topics for Data Structures and Algorithms

Just like programming, math is one of the core parts of learning data structures and algorithms. We mainly use math to analyse efficiency of various algorithms. But sometimes, the problem itself contains mathematical property or requires some mathematical insight to find a solution.

Tower of Hanoi Puzzle

Problem description of the tower of Hanoi: Given a stack of n disks arranged from largest on the bottom to smallest on top placed on a rod A, together with two empty rods B and C. The objective is to move the n disks from rod A to rod C using rod B.

Find prime numbers in a range: Sieve of Eratosthenes

The sieve of Eratosthenes is an ancient and efficient algorithm for finding all primes numbers from 2 to n. This algorithm finds all the prime numbers in a segment using O(nloglogn) operations.

Check if a number is prime or not: Primality Test

Given a positive integer n, write a program to check if the number is prime or not. A number n > 1 is said to be a prime number if 1 and n are its only factors. In other words, a prime number is a number that is divisible only by two numbers itself and one.

The Birthday Paradox

The birthday paradox is strange and counter-intuitive. It's a "paradox" because our brain find it difficult to handle the compounding power of exponents. Real-world applications for this include a cryptographic attack called the "birthday attack".

Find out the Fastest 3 Horses

There are 25 horses among which we need to find out the fastest 3 horses. In each race, only 5 horses can run simultaneously because there are only 5 tracks. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?