Leetcode-75 Sort Colors

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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.

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?

Example 1

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

解题思路

定义两个索引 i,j，i 之前全为 0，j 之后全为 2，[i,j] 之间未确定。采用第三个索引 p 来探索 [i,j]，若 nums[p]==0，交换 nums[p]、nums[i]，并使 i++；若 nums[p]==2，交换 nums[p]、nums[j]，并使 j--；若 nums[p]==1，考虑下一个元素。该思路的目标是将 0 交换到左边，2 交换到右边，使 1 留在中间。

复杂度分析

  • 时间复杂度：$O(n)$。
  • 空间复杂度：$O(1)$。

代码

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class Solution {
public:
	void sortColors(vector<int>& nums) {
		int n = nums.size();
		if (n == 0) return;
		int i = 0, j = n - 1, p = 0;
		while (p <= j) { //j之后已经合法
			if (p < i) p = i; //i之前已经合法,防止p对其造成破坏
			if (nums[p] == 0 && p != i) {
				swap(nums[p], nums[i]); //此处swap函数要求 p!=i
				i++;
			}
			else if (nums[p] == 2 && p != j) {
				swap(nums[p], nums[j]);
				j--;
			}
			else p++;
		}
	}
};