给定一个包含红色、白色和蓝色、共 n 个元素的数组 nums ，原地 对它们进行排序，使得相同颜色的元素相邻，并按照红色、白色、蓝色顺序排列。
我们使用整数 0、 1 和 2 分别表示红色、白色和蓝色。
必须在不使用库内置的 sort 函数的情况下解决这个问题。
https://leetcode.cn/problems/sort-colors/description/?envType=study-plan-v2&envId=top-100-liked

1. 归并排序

class Solution {

        public void doSort(int[] nums, int[] help,
                        int start, int end) {
        if (start >= end) {
            return;
        }
        int mid = (start + end) / 2;
        doSort(nums, help, start, mid);
        doSort(nums, help, mid + 1, end);

        int left = start;
        int right = mid + 1;

        int idx = left;
        while (left <= mid && right <= end) {
            if (nums[left] <= nums[right]) {
                help[idx++] = nums[left++];
            } else {
                help[idx++] = nums[right++];
            }
        }
        while (left <= mid) {
            help[idx++] = nums[left++];
        }
        while (right <= end) {
            help[idx++] = nums[right++];
        }

        for (int i = start; i <= end; i++) {
           nums[i] = help[i];
        }
    }


    public void sortColors(int[] nums) {
         int[] help = new int[nums.length];
        doSort(nums, help, 0, nums.length - 1);
    }
}

2. 计数

class Solution {

    

    public void sortColors(int[] nums) {
        int[] arr = new int[]{0,0,0};

        for (int i = 0; i < nums.length; i++) {
            arr[nums[i]] +=1;
        }
        
        int idx = 0;
        for (int i = 0; i < arr.length; i++) {
            while(arr[i]-- > 0) {
                nums[idx++] = i;
            }
        }
    }
}

3. 按照题目要求，原地腾挪

class Solution {

    private void swap(int[] nums, int left, int right) {
        int temp = nums[left];
        nums[left] = nums[right];
        nums[right] = temp;
    }

/**
 * zero side [0,zeroSide)
 * one side (zeroRSide, oneRSide)
 * two side (oneRSide, twoRSide)
 */
    public void sortColors(int[] nums) {

        int zeroRSide = 0;
        int oneRSide = 0;
        int twoRSide = 0;

        int cursor = 0;
        while (cursor < nums.length) {
            if (nums[cursor] == 0) {
                swap(nums, cursor, oneRSide);
                twoRSide += 1;
                swap(nums, oneRSide, zeroRSide);
                zeroRSide += 1;
                oneRSide += 1;
            } else if (nums[cursor] == 1) {
                swap(nums, cursor, oneRSide);
                oneRSide+=1;
                twoRSide+=1;
            } else {
                twoRSide += 1;
            }

            cursor += 1;
        }
    }
}