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In this article, we will learn how to find the minimum sum of factors of a given number. The key insight is that the minimum sum is achieved by using the sum of prime factors of the number. Problem Statement Given a number, find the minimum sum of factors that can multiply to give the original number. For example, the number 12 can be expressed as: 12 = 12 (sum = 12) 12 = 6 × 2 (sum = 8) 12 = 4 × 3 (sum = 7) 12 = 3 × 2 × 2 (sum ... Read More
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this article, we will learn different approaches to compute the nth Fibonacci number in Python. Problem statement − Our task is to compute the nth Fibonacci number. The sequence Fn of Fibonacci numbers is given by the recurrence relation: Fn = Fn-1 + Fn-2 with seed values: F0 = 0 and F1 = 1 We have two main approaches to solve this problem: Recursive approach Dynamic programming approach Using Recursive ... Read More
In this article, we will learn how to find the difference between the sum of odd digits and sum of even digits in a number, and check if this difference equals zero. Problem Statement − Given an integer, we need to calculate if the difference between the sum of odd digits and sum of even digits is 0 or not. Method 1: Brute Force Approach The straightforward approach calculates the sum of all even and odd digits separately, then finds their difference ? def difference_odd_even_digits(n): n = abs(n) # Handle ... Read More
In this article, we will learn how to calculate the cube sum of first n natural numbers using two different approaches. The cube sum series is: 1³ + 2³ + 3³ + 4³ + ... + n³. Problem statement − Given an input n, we need to print the sum of series 1³ + 2³ + 3³ + 4³ + ... + n³ till n-th term. Here we will discuss two approaches to solve this problem ? Brute-force approach using loops Mathematical solution using the sum formula Using Loop (Iterative Approach) This approach ... Read More
In this article, we will learn how to calculate compound interest using Python. Compound interest is the interest calculated on both the initial principal and the accumulated interest from previous periods. Problem statement − We are given three input values: principal amount, interest rate, and time period. We need to compute the compound interest. Formula The formula for calculating compound interest is: Compound Interest = P × (1 + R/100)^T Where: P is the principal amount (initial investment) R is the annual interest rate (in percentage) T is the time period (in ... Read More
A Z-form traversal of a square matrix follows a specific pattern: traverse the first row, then the main diagonal (excluding elements already printed), and finally the last row. This creates a Z-like path through the matrix. Understanding Z-Form Pattern For a matrix of size n×n, Z-form traversal involves three steps − Print all elements of the first row Print diagonal elements from top-right to bottom-left (excluding corners) Print all elements of the last row ... Read More
In this article, we will learn how to calculate the sum of the mathematical series 1/1! + 2/2! + 3/3! + 4/4! +.......+ n/n!, where each term is the ratio of a number to its factorial. Problem statement − Given an integer input n, we need to find the sum of the series 1/1! + 2/2! + 3/3! + 4/4! +.......+ n/n! Understanding the Series This series has an interesting mathematical property − as n approaches infinity, the sum converges to the mathematical constant e (approximately 2.718). Each term follows the pattern i/i! where i ranges from ... Read More
In this article, we will learn how to calculate the area of a circle using Python. Given the radius of a circle, we need to find its area using a simple mathematical formula. The area of a circle can be calculated using the following formula ? Area = π × r² Where π (pi) is approximately 3.14159 and r is the radius of the circle. Method 1: Using a Simple Function Let's implement a basic function to calculate the area ? def findArea(r): PI = 3.14159 ... Read More
In this article, we will learn how to calculate simple interest using Python. Simple interest is a method to calculate the interest charge on a loan or deposit. Simple interest is calculated by multiplying the principal amount by the interest rate and the time period. Unlike compound interest, it doesn't include interest on previously earned interest. Formula The mathematical formula for simple interest is: Simple Interest = (P × T × R) / 100 Where: P = Principal amount (initial money) T = Time period (in years) R = Rate of interest ... Read More
In this article, we will learn about the selection sort algorithm and its implementation in Python. Selection sort is a simple comparison-based sorting algorithm that works by finding the minimum element from the unsorted portion and placing it at the beginning. How Selection Sort Works The selection sort algorithm maintains two subarrays during execution: The subarray which is already sorted (initially empty) The subarray which is unsorted (initially the entire array) During each iteration, selection sort finds the minimum element from the unsorted subarray and swaps it with the first element of the unsorted ... Read More