Problem Description

A permutation of an array of integers is an arrangement of its members into a sequence or linear order.

• For example, for arr = [1,2,3], the following are all the permutations of arr: [1,2,3], [1,3,2], [2, 1, 3], [2, 3, 1], [3,1,2], [3,2,1].

The next permutation of an array of integers is the next lexicographically greater permutation of its integer. More formally, if all the permutations of the array are sorted in one container according to their lexicographical order, then the next permutation of that array is the permutation that follows it in the sorted container. If such arrangement is not possible, the array must be rearranged as the lowest possible order (i.e., sorted in ascending order).

• For example, the next permutation of arr = [1,2,3] is [1,3,2].
• Similarly, the next permutation of arr = [2,3,1] is [3,1,2].
• While the next permutation of arr = [3,2,1] is [1,2,3] because [3,2,1] does not have a lexicographical larger rearrangement.

Given an array of integers nums, find the next permutation of nums.

The replacement must be in place and use only 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]

Solution

The key observation is that for an array of numbers in descending order, there is NO next larger permutation. Therefore, we scan from right to left until we get an index i such that nums[i]<nums[i+1], then i is the index we want to replace with a just larger number in the nums[i+1:end]. Note that nums[i+1:end] is a sorted array in descending order, even after we swap nums[i] with its next larger number, which is another observation to help us find this next larger number and do a quick sort.

Java Code

class Solution {
    public void nextPermutation(int[] nums) {
        int len = nums.length, pvt=len-2;
        if(len == 1) return;
        while(pvt>=0 && nums[pvt]>= nums[pvt+1]) pvt--;
        if(pvt >= 0){
            int swap_idx = len-1;
            while(nums[swap_idx] <= nums[pvt]) swap_idx--;
            swap(nums, pvt, swap_idx);
        }
        int l = pvt<0 ? 0 : pvt+1, r = len-1;
        while(l < r){
            swap(nums, l, r);
            l++;
            r--;
        }
        return;
    }

    private void swap(int[] nums, int l, int r){
        int tmp = nums[l];
        nums[l] = nums[r];
        nums[r] = tmp;
    }
}