From 81f4b13a369cc6a14328ea5908334c19fe6252a9 Mon Sep 17 00:00:00 2001 From: Jojo Date: Fri, 17 Jan 2020 02:15:45 -0800 Subject: [PATCH] feat: #75 A better solution with O(n) (#280) * Update 75: A better solution with O(n) * Update 75.sort-colors.md * Update 75.sort-colors.md Co-authored-by: lucifer --- problems/75.sort-colors.md | 122 +++++++++++++++---------------------- 1 file changed, 50 insertions(+), 72 deletions(-) diff --git a/problems/75.sort-colors.md b/problems/75.sort-colors.md index e682d070d..1282b9ec1 100644 --- a/problems/75.sort-colors.md +++ b/problems/75.sort-colors.md @@ -19,77 +19,55 @@ First, iterate the array counting number of 0's, 1's, and 2's, then overwrite ar Could you come up with a one-pass algorithm using only constant space? ## 思路 +这个问题是典型的荷兰国旗问题 （https://en.wikipedia.org/wiki/Dutch_national_flag_problem）。 因为我们可以将红白蓝三色小球想象成条状物，有序排列后正好组成荷兰国旗。 -其实就是排序，而且没有要求稳定性，就是用啥排序算法都行。 -题目并没有给出数据规模，因此我默认数据量不大，直接选择了冒泡排序 - -## 关键点解析 - -冒泡排序的时间复杂度是N平方，无法优化，但是可以进一步优化常数项， -比如循环的起止条件。 由于每一次遍历都会将最后一位“就位”，因此内层循环的截止条件就可以是 - `nums.length - i`， 而不是 `nums.length`, 可以省一半的时间。 - - -## 代码 - -```js -/* - * @lc app=leetcode id=75 lang=javascript - * - * [75] Sort Colors - * - * https://leetcode.com/problems/sort-colors/description/ - * - * algorithms - * Medium (41.41%) - * Total Accepted: 297K - * Total Submissions: 716.1K - * Testcase Example: '[2,0,2,1,1,0]' - * - * 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? - * - * - */ -/** - * @param {number[]} nums - * @return {void} Do not return anything, modify nums in-place instead. - */ -var sortColors = function(nums) { - function swap(nums, i, j) { - const temp = nums[i]; - nums[i] = nums[j]; - nums[j] = temp; - } - for (let i = 0; i < nums.length - 1; i++) { - for (let j = 0; j < nums.length - i; j++) { - if (nums[j] < nums[j -1]) { - swap(nums, j - 1 , j) - } - - } - } -}; +有两种解决思路。 + +## 解法一 +- 遍历数组，统计红白蓝三色球（0，1，2）的个数 +- 根据红白蓝三色球（0，1，2）的个数重排数组 + +这种思路的时间复杂度：$O(n)$，需要遍历数组两次。 + +## 解法二 + +我们可以把数组分成三部分，前部（全部是0），中部（全部是1）和后部（全部是2）三个部分。每一个元素（红白蓝分别对应0、1、2）必属于其中之一。将前部和后部各排在数组的前边和后边，中部自然就排好了。 + +我们用三个指针，设置两个指针begin指向前部的末尾的下一个元素（刚开始默认前部无0，所以指向第一个位置），end指向后部开头的前一个位置（刚开始默认后部无2，所以指向最后一个位置），然后设置一个遍历指针current，从头开始进行遍历。 + +这种思路的时间复杂度也是$O(n)$, 只需要遍历数组一次。 + +### 关键点解析 + + +- 荷兰国旗问题 +- counting sort + +### 代码 + +代码支持： Python3 + +Python3 Code: + +``` python +class Solution: + def sortColors(self, nums: List[int]) -> None: + """ + Do not return anything, modify nums in-place instead. + """ + p0 = cur = 0 + p2 = len(nums) - 1 + + while cur <= p2: + if nums[cur] == 0: + nums[cur], nums[p0] = nums[p0], nums[cur] + p0 += 1 + cur += 1 + elif nums[cur] == 2: + nums[cur], nums[p2] = nums[p2], nums[cur] + p2 -= 1 + else: + cur += 1 ``` + +