daily leetcode - sort-colors - !

题目地址

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

题目描述

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?

思路

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(3);
        for (int num : nums) ++colors[num];
        for (int i = 0, cur = 0; i < 3; ++i) {
            for (int j = 0; j < colors[i]; ++j) {
                nums[cur++] = i;
            }
        }
    }
};

题目中还要让只遍历一次数组来求解,那么我需要用双指针来做,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 = 0, blue = (int)nums.size() - 1;
        for (int i = 0; i <= blue; ++i) {
            if (nums[i] == 0) {
                swap(nums[i], nums[red++]);
            } else if (nums[i] == 2) {
                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 = 0, right = (int)nums.size() - 1, cur = 0;
        while (cur <= right) {
            if (nums[cur] == 0) {
                swap(nums[cur++], nums[left++]);
            } else if (nums[cur] == 2) {
                swap(nums[cur], nums[right--]);
            } else {
                ++cur;
            }
        }
    }
};

思路2

  • 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

/*
 * @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)
            }
            
        }      
    }
};

本文参考自:
https://github.com/grandyang/leetcode/ &
https://github.com/azl397985856/leetcode


标题: daily leetcode - sort-colors - !
文章作者: lonuslan
文章链接: https://louislan.com/articles/2020/02/17/1581921734150.html
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