[LeetCode] 75. Sort Colors (Quick Sort)

1. Description

Given an array with n objects colored red, white or blue, sort them in-place so that objects of the same color are adjacent, with the colors in the order red, white and blue.

Here, we will use the integers 0, 1, and 2 to represent the color red, white, and blue respectively.

Note: You are not suppose to use the library’s sort function for this problem.

Example:

Input: [2,0,2,1,1,0]
Output: [0,0,1,1,2,2]

Follow up:

A rather straight forward solution is a two-pass algorithm using counting sort.
First, iterate the array counting number of 0’s, 1’s, and 2’s, then overwrite array with total number of 0’s, then 1’s and followed by 2’s.
Could you come up with a one-pass algorithm using only constant space?

2. Method

Quick Sort

1. pick an element as pivot (always the first element)
2. put all elements that lass than or equal before the pivot
3. put all elements that bigger than pivot behind it
4. divide and conquer

实现代码

class Solution {
    public void sortColors(int[] nums) {
        quickSort(nums, 0, nums.length-1);
        return;
    }
    //Quick Sort
    public void quickSort(int[] nums, int l, int r){
        if(r <= l){
            return;
        }
        int x = nums[l];
        int i = l;
        int j = r;
        
        //make all elements behind i are bigger or equal x
        //make all elements before i are less x
        while(i < j){
            //from tail to head
            while(i < j && nums[j] >= x){
                j--;
            }
            if(i < j){
                nums[i] = nums[j]; 
                i++;
            }
        
            //from head to tail
            while(i < j && nums[i] < x){
                i++;
            }
            if(i < j){
                nums[j] = nums[i];
                j--;
            }
        }
        
        //when i == j
        nums[i] = x;
        
        //next, we need to divide and conquer
        quickSort(nums, l, i-1);
        quickSort(nums, i+1, r);
    }
}