【leetcode】75. Sort Colors

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本文深入探讨了LeetCode上经典问题“Sort Colors”的多种解决方案，包括两头夹逼法、平移插入法及三路快排。通过这些方法，文章详细讲解了如何在不使用库排序函数的情况下，对红、白、蓝三种颜色的对象进行排序。

75. Sort Colors

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?

题目链接：https://leetcode.com/problems/sort-colors/

1.两头夹逼法（非in-place）：

双指针对0和2进行排序，一个指向0的最后一位，一个指向2的第一位，都从数组两端向中间移动。

对原始数组进行遍历，

class Solution {
public:
    void sortColors(vector<int>& nums) {
        int len = nums.size();
        int l = 0, r = len - 1;
        vector<int> res(len);
        for (int i = 0; i < len; ++i){
            if (nums[i] == 0){
                res[l++] = 0;
            }else if (nums[i] == 2){
                res[r--] = 2;
            }
        }
        while (l <= r){
            res[l++] = 1;
        }
        return res;
    }
};

2.平移插入法（one pass的计数排序）

每一种颜色对应一个指针，记录在排序数组中对应颜色的最后一个元素的位置。

class Solution {
public:
    void sortColors(vector<int> A) {
        int i = -1;
        int j = -1;
        int k = -1;
        int n = A.size();
        for(int p = 0; p < n; p ++)
        {
            //根据第i个数字，挪动0~i-1串。
            if(A[p] == 0)
            {
                A[++k] = 2;    //2往后挪
                A[++j] = 1;    //1往后挪
                A[++i] = 0;    //0往后挪
            }
            else if(A[p] == 1)
            {
                A[++k] = 2;
                A[++j] = 1;
            }
            else
                A[++k] = 2;
        }

    }
};

3.三路排序

如果颜色种类很多，就当作排序算法来做。一般数组有较多重复元素的，会使用三路快排，好像也是java里排序算法的实现。

class Solution {
public:
    void sortColors(vector<int>& nums) {
        int len = nums.size();
        int l = -1, r = len;
        for(int i = 0; i<r;){
            if (nums[i] == 0){
                swap(nums[++l], nums[i++]);
            }else if(nums[i] == 2){
                swap(nums[--r], nums[i]);
            }else{
                ++i;
            }
        }
    }
};