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Math Basics

A collection of 23 posts

Number System

What is a number? A number is a mathematical object used to count, measure, and label. Numbers are also used to represent quantities and make calculations. For example, we use numbers in everyday life to count money, time, and things. Numbers themselves are categorized into various types, such as Natural

Logarithm basics for DSA Solution In C++/Java/Python/JS

What is a Logarithm? Description A logarithm is the inverse operation of exponentiation. It determines the power to which a given base must be raised to obtain a specified number. Mathematically, if: b^x = y Then, using logarithms: logb y = x This is read as "logarithm of y to

Find the AP/GP/HP Solution In C++/Java/Python/JS

When preparing for DSA interviews, we often come across number sequences. Three common types are: * Arithmetic Progression (AP) – where the difference between consecutive terms is constant. * Geometric Progression (GP) – where the ratio between consecutive terms is constant. * Harmonic Progression (HP) – where the reciprocals of the terms form an AP. Understanding

Find the Mean/Median/Mode of the Given Array Solution In C++/Java/Python/JS

Description Statistical measures help us understand data distribution and central tendency. When analyzing data, we often need to find representative values that summarize the entire dataset. The three most common statistical measures are: 1. Mean: The arithmetic average of all values in the array. 2. Median: The middle value when

Check if an Integer is a Power of 2/3/4/5... Solution In C++/Java/Python/JS

Problem Description: Given an integer n, check if it is a power of 2, 3, 4, 5.... Return True if it is, otherwise return False. Examples: Input: n = 16 Output: True Explanation: 16 is a power of 2 and 4. Input: n = 27 Output: True Explanation: 27 is a power

Implement Power function (pow(x,n)) question description

Implement Power Function (pow(x,n)) Solution in C++/Java/Python/JS

Description Implement pow(x,n), which calculates x raised to the power n (i.e., xn). Examples Input: x = 2.00000, n = 10 Output: 1024.00000 Input: x = 2.10000, n = 3 Output: 9.26100 Input: x = 2.00000, n = -2 Output: 0.25000 Explanation: 2-2 = 1/22 = 1/4

How to Find nPr and nCr Solution In C++/Java/Python/JS

Introduction In the journey of learning Data Structures and Algorithms (DSA), we often come across problems that require counting arrangements, selections, or groupings. Whether it's calculating possibilities in recursion, brute force combinations, or logic puzzles, one concept keeps popping up — Permutation and Combination. Understanding this topic early will

How to Find Ceil and Floor Solution In C++/Java/Python/JS

How to find Ceil and Floor Problem Description Given a real number x, find: Ceil of x: The smallest integer that is greater than or equal to x. Floor of x: The largest integer that is less than or equal to x. You must return both values as output. Examples:

Check Divisibility Rules for Numbers from 1 to 20

In this article, we'll take a closer look at divisibility rules. These are simple tricks that help you quickly determine if one number can be divided by another, without actually doing the division. These rules are really helpful for mental math, allowing you to solve problems faster, whether

Perform Modulo Operations

Introduction When dividing a number a by another number b, the result can either be a complete division with no remainder or leave a remainder. For instance, consider dividing 15 by 5: 15÷5=3 with no remainder. Here, 15 is divided by 5 with a quotient of 3 and

Find All Divisors of a Given Number

In this section, we will explore how to find all the divisors of a given number n. What is the divisor of a number? Divisors of a given number n are the numbers that divide n evenly without leaving a remainder. In other words, if n is divisible by k,

Check if two numbers are co-prime or not Solution In C++/Java/Python/JS

Description Two numbers A and B are said to be Co-Prime or mutually prime if the Greatest Common Divisor of them is 1. You have been given two numbers A and B, find if they are Co-prime or not. Example Input : 2 3 Output : Co-Prime Input : 4 8 Output : Not

Check if a number is prime without using the Sieve of Eratosthenes Solution In C++/Java/Python/JS

What exactly is a prime number? A prime number is a number that is greater than 1 and has only two factors: 1 and itself. In other words, a prime number is not divisible by any other numbers except 1 and itself. For example: * 7 is a prime number because

Calculate the LCM and GCD of Two Numbers Solution In C++/Java/Python/JS

Problem Description: Given two integers A and B, find their Greatest Common Divisor (GCD) and Least Common Multiple (LCM). The GCD (Greatest Common Divisor) of two numbers is the largest number that divides both A and B without leaving a remainder. The LCM (Least Common Multiple) of two numbers is

Find the Number of Trailing Zeroes in the Factorial of a Given Number n

Examples : Input: 5 Output: 1 Explanation: A factorial of 5 is 120, so it had only 1 trailing zero. Input: 10 Output: 2 Explanation: A factorial of 5 is 3628800, so it had only 2 trailing zeros. 💡Try it yourself first! Intuition The brute force approach to this question is

Calculate the Factorial of a Number

The factorial of a non-negative integer n is a mathematical function denoted by n! It represents the product of all positive integers from 1 up to n. Examples : Input: 5 Output: 120 Explanation: 5! is equal to 5*4*3*2*1 = 120. Input: 4 Output: 24 Explanation: 4! is

Generate Fibonacci Numbers up to a Given Limit Solution in C++/Java/Python/JS

A Fibonacci number is part of a sequence of numbers known as the Fibonacci sequence, which is characterized by the fact that every number after the first two is the sum of the two preceding ones. The sequence starts with 0 and 1, and from there, each subsequent number is

Count the occurrences of digit '1' in all numbers from 1 to n

Count the Occurrences of Digit '1' in All Numbers from 1 to n Solution In C++/Java/Python/JS

Problem Description: Given an integer n, count the occurrences of the digit '1' in all numbers from 1 to n. Examples: Input: n = 13 Output: 6 Explanation: The numbers containing '1' are 1, 10, 11, 12, 13. The total count is 6. Example 2: Input: n

Armstrong Number

Check if a Number is an Armstrong Number

Given a non-negative integer num, check whether the given number is an Armstrong number or not. An Armstrong number is a number that is equal to the sum of its digits each raised to the power of the number of digits in the number. Examples : Input: 1634 Output: true Explanation:

check palindrome

Check if a Number is a Palindrome

Given a non-negative integer num, check whether the given number is palindrome or not. What is a palindrome? A palindrome is a word, phrase, number, or any other sequence of characters that reads the same forward and backward. Examples Input: 121 Output: true Explanation: The number 121 reads the same

Reverse a Given Number

Given an integer num, reverse the digits of the number and return the reversed number. Examples Input: 687 Output: 786 Explanation: If we reverse the number 687, we will get 786. Input: 120 Output: 21 Explanation: If we reverse the number 120, we will get 021 so after removing trailing

Find the Sum of Digits of a Number

Given a number num, find the sum of digits of the number. What is the "Sum Of Digits of A Number" Input: 687 Output: 21 Explanation: The sum of digits i.e. 6 + 8 + 7 is equal to 21. Input: 12 Output: 3 Explanation: The Sum Of Digits

Introduction to Basic Math

Before diving into the world of programming, it's essential to build a strong foundation in mathematics, In this section, we will walk through fundamental mathematical concepts in a structured manner, ensuring that you not only understand them but also see how they apply to real-world programming challenges. Hold