[LeetCode] 75. Sort Colors 颜色排序

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?

 

这道题的本质还是一道排序的题，题目中给出提示说可以用计数排序，需要遍历数组两遍，那么先来看这种方法，因为数组中只有三个不同的元素，所以实现起来很容易。

- 首先遍历一遍原数组，分别记录 0，1，2 的个数。
- 然后更新原数组，按个数分别赋上 0，1，2。

解法一：

class Solution {
public:
    void sortColors(vector<int>& nums) {
        vector<int> colors();
        for (int num : nums) ++colors[num];
        for (int i = , cur = ; i < ; ++i) {
            for (int j = ; j < colors[i]; ++j) {
                nums[cur++] = i;
            }
        }
    }
};

题目中还要让只遍历一次数组来求解，那么就需要用双指针来做，分别从原数组的首尾往中心移动。

- 定义 red 指针指向开头位置，blue 指针指向末尾位置。

- 从头开始遍历原数组，如果遇到0，则交换该值和 red 指针指向的值，并将 red 指针后移一位。若遇到2，则交换该值和 blue 指针指向的值，并将 blue 指针前移一位。若遇到1，则继续遍历。

解法二：

class Solution {
public:
    void sortColors(vector<int>& nums) {
        int red = , blue = (int)nums.size() - ;
        for (int i = ; i <= blue; ++i) {
            if (nums[i] == ) {
                swap(nums[i], nums[red++]);
            } else if (nums[i] == ) {
                swap(nums[i--], nums[blue--]);
            }
        }
    }
};

当然我们也可以使用 while 循环的方式来写，那么就需要一个变量 cur 来记录当前遍历到的位置，参见代码如下：

解法三：

class Solution {
public:
    void sortColors(vector<int>& nums) {
        int left = , right = (int)nums.size() - , cur = ;
        while (cur <= right) {
            if (nums[cur] == ) {
                swap(nums[cur++], nums[left++]);
            } else if (nums[cur] == ) {
                swap(nums[cur], nums[right--]);
            } else {
                ++cur;
            }
        }
    }
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/75

类似题目：

Sort List

Wiggle Sort II

Wiggle Sort

参考资料：

https://leetcode.com/problems/sort-colors/

https://leetcode.com/problems/sort-colors/discuss/26500/Four-different-solutions

https://leetcode.com/problems/sort-colors/discuss/26472/Share-my-at-most-two-pass-constant-space-10-line-solution

https://leetcode.com/problems/sort-colors/discuss/26760/C%2B%2B-solution-in-8-lines%3A-an-instance-of-the-Dutch-national-flag-problem-by-Edsger-Dijkstra

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