Next Permutation Explained Step by Step

Introduction In many problems, we need to rearrange numbers into the next possible greater order. This is known as the next permutation. This problem is important because it teaches how to manipulate arrays efficiently without generating all permutations. Problem Statement Given an array of integers nums, rearrange it into the next lexicographically greater permutation. If such an arrangement is not possible, rearrange it into the lowest possible order (ascending order). The rearrangement must be done in-place using constant extra memory. Example 1: Input: nums = [1, 2, 3] Output: [1, 3, 2] Example 2: Input: nums = [3, 2, 1] Output: [1, 2, 3] Explanation: This is the last permutation, so we return the smallest. Understanding the Idea The goal is to find the next greater arrangement of numbers. Instead of generating all permutations, we follow a pattern. Step-by-Step Approach Step 1: Find the breakpoint Traverse from right to left and find the first index i such that: nums[i] < nums[