1. Problem Statement (Simple Explanation): You’re given two non-negative integers num1 and num2 as strings . You must: Return their product as a string . You cannot : Use built-in big integer libraries. Convert the entire strings directly to integers. Lengths: 1 <= len(num1), len(num2) <= 200 Digits only, no leading zero except "0" itself. 2. Examples: Example 1: Input: num1 = "2", num2 = "3" 2 * 3 = 6 Output: "6" Example 2: Input: num1 = "123", num2 = "456" 123 * 456 = 56088 Output: "56088" 3. Intuition – Simulate Grade-School Multiplication: We multiply like on paper: For num1 = "123", num2 = "456": 1 2 3 x 4 5 6 --------- 7 3 8 (123 * 6, shifted by 0) 6 1 5 (123 * 5, shifted by 1) 4 9 2 (123 * 4, shifted by 2) --------- 5 6 0 8 8 But instead of summing separate rows, we can direct...
Cycle sort is a comparison-based sorting algorithm that is designed to minimize the number of writes. It works by dividing the input sequence into cycles, and then for each cycle, it finds the correct position for each element by performing a series of swaps. This algorithm has a time complexity of O(n^2), but it is very efficient when the number of writes is a concern. The main idea behind cycle sort is to minimize the number of writes by moving each element to its correct position without unnecessary swaps. This is achieved by dividing the input sequence into cycles, where each cycle is a permutation of a subset of the elements in the input sequence. For example, if the input sequence is [4, 1, 5, 3, 2], the cycles would be [4, 2], [1], [5], [3]. For each cycle, cycle sort finds the correct position for each element by performing a series of swaps. It starts by selecting the smallest element in the cycle, and then it swaps it with the element that should be in its correct position. I...