Next Permutation

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers.

If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order).

The replacement must be in-place, do not allocate extra memory.

Here are some examples. Inputs are in the left-hand column and its corresponding outputs are in the right-hand column. 1,2,3 → 1,3,2 3,2,1 → 1,2,3 1,1,5 → 1,5,1

Idea:

1. Reverse find first number which breaks descending order.
2. Exchange this number with the least number that’s greater than this number.
3. Reverse sort the numbers after the exchanged number.

Solution:

/*
    Idea:
    1. Reverse find first number which breaks descending order.
    2. Exchange this number with the least number that's greater than this number.
    3. Reverse sort the numbers after the exchanged number.
*/

public class Solution {
    public void nextPermutation(int[] nums) {
        /* 1. Reverse find first number which breaks descending order. */
        int i=nums.length-1;
        for(; i>=1; i--)
            if(nums[i-1]<nums[i]) break;
        
        /* if no break found in step 1 */
        if(i==0){
            /* for case "1" and "1111" */
            if(nums.length==1 || nums[0]==nums[1]) return; 
            /* for case "54321" */
            int lo=i, hi=nums.length-1; 
            while(lo<hi) swap(nums, lo++, hi--);
            return;
        }
        
        /* 2. Exchange this number with the least number that's greater than this number. */
        /* 2.1 Find the least number that's greater using binary search, O(log(nums.length-i)) */
        int j = binarySearchLeastGreater(nums, i, nums.length-1, nums[i-1]);
        
        /* 2.2 Exchange the numbers */
        if(j!=-1) swap(nums, i-1, j);
        
        /* 3. Reverse sort the numbers after the exchanged number. */
        int lo=i, hi=nums.length-1;
        while(lo<hi) swap(nums, lo++, hi--);
    }
    
    public int binarySearchLeastGreater(int[] nums, int lo, int hi, int key){
        while(lo<=hi){
            int mid = lo + (hi-lo)/2;
            if(nums[mid]>key){
                lo = mid+1;
            } else {
                hi = mid-1;
            }
        }
        return hi;
    }
    
    public void swap(int[] nums, int i, int j){
        int tmp = nums[j];
        nums[j] = nums[i];
        nums[i] = tmp;
    }
}