630 lines
17 KiB
Markdown
630 lines
17 KiB
Markdown
<p align="center">
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<a href="https://programmercarl.com/other/xunlianying.html" target="_blank">
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<img src="../pics/训练营.png" width="1000"/>
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</a>
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<p align="center"><strong><a href="https://mp.weixin.qq.com/s/tqCxrMEU-ajQumL1i8im9A">参与本项目</a>，贡献其他语言版本的代码，拥抱开源，让更多学习算法的小伙伴们收益！</strong></p>
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## 59.螺旋矩阵II
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[力扣题目链接](https://leetcode.cn/problems/spiral-matrix-ii/)
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给定一个正整数 n，生成一个包含 1 到 n^2 所有元素，且元素按顺时针顺序螺旋排列的正方形矩阵。
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示例:
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输入: 3
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输出:
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[
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[ 1, 2, 3 ],
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[ 8, 9, 4 ],
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[ 7, 6, 5 ]
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]
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## 思路
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为了利于录友们理解，我特意录制了视频，[拿下螺旋矩阵！LeetCode：59.螺旋矩阵II](https://www.bilibili.com/video/BV1SL4y1N7mV)，结合视频一起看，事半功倍！
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这道题目可以说在面试中出现频率较高的题目，**本题并不涉及到什么算法，就是模拟过程，但却十分考察对代码的掌控能力。**
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要如何画出这个螺旋排列的正方形矩阵呢？
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相信很多同学刚开始做这种题目的时候，上来就是一波判断猛如虎。
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结果运行的时候各种问题，然后开始各种修修补补，最后发现改了这里那里有问题，改了那里这里又跑不起来了。
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大家还记得我们在这篇文章[数组：每次遇到二分法，都是一看就会，一写就废](https://programmercarl.com/0704.二分查找.html)中讲解了二分法，提到如果要写出正确的二分法一定要坚持**循环不变量原则**。
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而求解本题依然是要坚持循环不变量原则。
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模拟顺时针画矩阵的过程:
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* 填充上行从左到右
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* 填充右列从上到下
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* 填充下行从右到左
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* 填充左列从下到上
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由外向内一圈一圈这么画下去。
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可以发现这里的边界条件非常多，在一个循环中，如此多的边界条件，如果不按照固定规则来遍历，那就是**一进循环深似海，从此offer是路人**。
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这里一圈下来，我们要画每四条边，这四条边怎么画，每画一条边都要坚持一致的左闭右开，或者左开右闭的原则，这样这一圈才能按照统一的规则画下来。
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那么我按照左闭右开的原则，来画一圈，大家看一下：
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这里每一种颜色，代表一条边，我们遍历的长度，可以看出每一个拐角处的处理规则，拐角处让给新的一条边来继续画。
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这也是坚持了每条边左闭右开的原则。
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一些同学做这道题目之所以一直写不好，代码越写越乱。
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就是因为在画每一条边的时候，一会左开右闭，一会左闭右闭，一会又来左闭右开，岂能不乱。
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代码如下，已经详细注释了每一步的目的，可以看出while循环里判断的情况是很多的，代码里处理的原则也是统一的左闭右开。
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整体C++代码如下：
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```CPP
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class Solution {
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public:
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vector<vector<int>> generateMatrix(int n) {
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vector<vector<int>> res(n, vector<int>(n, 0)); // 使用vector定义一个二维数组
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int startx = 0, starty = 0; // 定义每循环一个圈的起始位置
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int loop = n / 2; // 每个圈循环几次，例如n为奇数3，那么loop = 1 只是循环一圈，矩阵中间的值需要单独处理
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int mid = n / 2; // 矩阵中间的位置，例如：n为3， 中间的位置就是(1，1)，n为5，中间位置为(2, 2)
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int count = 1; // 用来给矩阵中每一个空格赋值
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int offset = 1; // 需要控制每一条边遍历的长度，每次循环右边界收缩一位
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int i,j;
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while (loop --) {
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i = startx;
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j = starty;
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// 下面开始的四个for就是模拟转了一圈
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// 模拟填充上行从左到右(左闭右开)
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for (j = starty; j < n - offset; j++) {
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res[startx][j] = count++;
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}
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// 模拟填充右列从上到下(左闭右开)
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for (i = startx; i < n - offset; i++) {
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res[i][j] = count++;
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}
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// 模拟填充下行从右到左(左闭右开)
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for (; j > starty; j--) {
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res[i][j] = count++;
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}
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// 模拟填充左列从下到上(左闭右开)
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for (; i > startx; i--) {
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res[i][j] = count++;
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}
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// 第二圈开始的时候，起始位置要各自加1， 例如：第一圈起始位置是(0, 0)，第二圈起始位置是(1, 1)
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startx++;
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starty++;
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// offset 控制每一圈里每一条边遍历的长度
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offset += 1;
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}
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// 如果n为奇数的话，需要单独给矩阵最中间的位置赋值
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if (n % 2) {
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res[mid][mid] = count;
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}
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return res;
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}
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};
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```
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## 类似题目
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* 54.螺旋矩阵
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* 剑指Offer 29.顺时针打印矩阵
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## 其他语言版本
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Java：
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```Java
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class Solution {
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public int[][] generateMatrix(int n) {
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int loop = 0; // 控制循环次数
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int[][] res = new int[n][n];
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int start = 0; // 每次循环的开始点(start, start)
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int count = 1; // 定义填充数字
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int i, j;
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while (loop++ < n / 2) { // 判断边界后，loop从1开始
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// 模拟上侧从左到右
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for (j = start; j < n - loop; j++) {
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res[start][j] = count++;
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}
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// 模拟右侧从上到下
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for (i = start; i < n - loop; i++) {
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res[i][j] = count++;
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}
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// 模拟下侧从右到左
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for (; j >= loop; j--) {
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res[i][j] = count++;
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}
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// 模拟左侧从下到上
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for (; i >= loop; i--) {
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res[i][j] = count++;
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}
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start++;
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}
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if (n % 2 == 1) {
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res[start][start] = count;
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}
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return res;
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}
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}
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```
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python3:
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```python
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class Solution:
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def generateMatrix(self, n: int) -> List[List[int]]:
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nums = [[0] * n for _ in range(n)]
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startx, starty = 0, 0 # 起始点
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loop, mid = n // 2, n // 2 # 迭代次数、n为奇数时，矩阵的中心点
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count = 1 # 计数
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for offset in range(1, loop + 1) : # 每循环一层偏移量加1，偏移量从1开始
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for i in range(starty, n - offset) : # 从左至右，左闭右开
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nums[startx][i] = count
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count += 1
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for i in range(startx, n - offset) : # 从上至下
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nums[i][n - offset] = count
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count += 1
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for i in range(n - offset, starty, -1) : # 从右至左
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nums[n - offset][i] = count
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count += 1
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for i in range(n - offset, startx, -1) : # 从下至上
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nums[i][starty] = count
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count += 1
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startx += 1 # 更新起始点
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starty += 1
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if n % 2 != 0 : # n为奇数时，填充中心点
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nums[mid][mid] = count
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return nums
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```
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javaScript
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```javascript
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/**
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* @param {number} n
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* @return {number[][]}
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*/
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var generateMatrix = function(n) {
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let startX = startY = 0; // 起始位置
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let loop = Math.floor(n/2); // 旋转圈数
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let mid = Math.floor(n/2); // 中间位置
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let offset = 1; // 控制每一层填充元素个数
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let count = 1; // 更新填充数字
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let res = new Array(n).fill(0).map(() => new Array(n).fill(0));
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while (loop--) {
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let row = startX, col = startY;
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// 上行从左到右（左闭右开）
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for (; col < startY + n - offset; col++) {
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res[row][col] = count++;
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}
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// 右列从上到下（左闭右开）
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for (; row < startX + n - offset; row++) {
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res[row][col] = count++;
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}
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// 下行从右到左（左闭右开）
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for (; col > startY; col--) {
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res[row][col] = count++;
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}
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// 左列做下到上（左闭右开）
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for (; row > startX; row--) {
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res[row][col] = count++;
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}
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// 更新起始位置
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startX++;
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startY++;
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// 更新offset
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offset += 2;
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}
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// 如果n为奇数的话，需要单独给矩阵最中间的位置赋值
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if (n % 2 === 1) {
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res[mid][mid] = count;
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}
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return res;
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};
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```
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TypeScript:
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```typescript
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function generateMatrix(n: number): number[][] {
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let loopNum: number = Math.floor(n / 2);
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const resArr: number[][] = new Array(n).fill(1).map(i => new Array(n));
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let chunkNum: number = n - 1;
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let startX: number = 0;
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let startY: number = 0;
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let value: number = 1;
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let x: number, y: number;
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while (loopNum--) {
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x = startX;
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y = startY;
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while (x < startX + chunkNum) {
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resArr[y][x] = value;
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x++;
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value++;
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}
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while (y < startY + chunkNum) {
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resArr[y][x] = value;
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y++;
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value++;
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}
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while (x > startX) {
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resArr[y][x] = value;
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x--;
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value++;
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}
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while (y > startY) {
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resArr[y][x] = value;
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y--;
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value++;
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}
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startX++;
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startY++;
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chunkNum -= 2;
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}
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if (n % 2 === 1) {
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resArr[startX][startY] = value;
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}
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return resArr;
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};
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```
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Go:
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```go
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func generateMatrix(n int) [][]int {
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top, bottom := 0, n-1
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left, right := 0, n-1
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num := 1
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tar := n * n
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matrix := make([][]int, n)
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for i := 0; i < n; i++ {
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matrix[i] = make([]int, n)
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}
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for num <= tar {
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for i := left; i <= right; i++ {
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matrix[top][i] = num
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num++
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}
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top++
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for i := top; i <= bottom; i++ {
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matrix[i][right] = num
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num++
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}
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right--
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for i := right; i >= left; i-- {
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matrix[bottom][i] = num
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num++
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}
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bottom--
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for i := bottom; i >= top; i-- {
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matrix[i][left] = num
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num++
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}
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left++
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}
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return matrix
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}
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```
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Swift:
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```swift
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func generateMatrix(_ n: Int) -> [[Int]] {
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var result = [[Int]](repeating: [Int](repeating: 0, count: n), count: n)
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var startRow = 0
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var startColumn = 0
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var loopCount = n / 2
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let mid = n / 2
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var count = 1
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var offset = 1
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var row: Int
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var column: Int
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while loopCount > 0 {
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row = startRow
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column = startColumn
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for c in column ..< startColumn + n - offset {
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result[startRow][c] = count
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count += 1
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column += 1
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}
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for r in row ..< startRow + n - offset {
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result[r][column] = count
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count += 1
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row += 1
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}
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for _ in startColumn ..< column {
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result[row][column] = count
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count += 1
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column -= 1
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}
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for _ in startRow ..< row {
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result[row][column] = count
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count += 1
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row -= 1
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}
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startRow += 1
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startColumn += 1
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offset += 2
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loopCount -= 1
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}
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if (n % 2) != 0 {
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result[mid][mid] = count
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}
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return result
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}
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```
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Rust:
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```rust
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impl Solution {
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pub fn generate_matrix(n: i32) -> Vec<Vec<i32>> {
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let mut res = vec![vec![0; n as usize]; n as usize];
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let (mut startX, mut startY, mut offset): (usize, usize, usize) = (0, 0, 1);
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let mut loopIdx = n/2;
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let mid: usize = loopIdx as usize;
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let mut count = 1;
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let (mut i, mut j): (usize, usize) = (0, 0);
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while loopIdx > 0 {
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i = startX;
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j = startY;
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while j < (startY + (n as usize) - offset) {
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res[i][j] = count;
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count += 1;
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j += 1;
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}
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while i < (startX + (n as usize) - offset) {
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res[i][j] = count;
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count += 1;
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i += 1;
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}
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while j > startY {
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res[i][j] = count;
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count += 1;
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j -= 1;
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}
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while i > startX {
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res[i][j] = count;
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count += 1;
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i -= 1;
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}
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startX += 1;
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startY += 1;
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offset += 2;
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loopIdx -= 1;
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}
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if(n % 2 == 1) {
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res[mid][mid] = count;
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}
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res
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}
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}
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```
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PHP:
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```php
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class Solution {
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/**
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* @param Integer $n
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* @return Integer[][]
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*/
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function generateMatrix($n) {
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// 初始化数组
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$res = array_fill(0, $n, array_fill(0, $n, 0));
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$mid = $loop = floor($n / 2);
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$startX = $startY = 0;
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$offset = 1;
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$count = 1;
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while ($loop > 0) {
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$i = $startX;
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$j = $startY;
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for (; $j < $startY + $n - $offset; $j++) {
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$res[$i][$j] = $count++;
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}
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for (; $i < $startX + $n - $offset; $i++) {
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$res[$i][$j] = $count++;
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}
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for (; $j > $startY; $j--) {
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$res[$i][$j] = $count++;
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}
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for (; $i > $startX; $i--) {
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$res[$i][$j] = $count++;
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}
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$startX += 1;
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$startY += 1;
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$offset += 2;
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$loop--;
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}
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if ($n % 2 == 1) {
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$res[$mid][$mid] = $count;
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}
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return $res;
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}
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}
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```
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C:
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```c
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int** generateMatrix(int n, int* returnSize, int** returnColumnSizes){
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//初始化返回的结果数组的大小
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*returnSize = n;
|
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*returnColumnSizes = (int*)malloc(sizeof(int) * n);
|
||
//初始化返回结果数组ans
|
||
int** ans = (int**)malloc(sizeof(int*) * n);
|
||
int i;
|
||
for(i = 0; i < n; i++) {
|
||
ans[i] = (int*)malloc(sizeof(int) * n);
|
||
(*returnColumnSizes)[i] = n;
|
||
}
|
||
|
||
//设置每次循环的起始位置
|
||
int startX = 0;
|
||
int startY = 0;
|
||
//设置二维数组的中间值，若n为奇数。需要最后在中间填入数字
|
||
int mid = n / 2;
|
||
//循环圈数
|
||
int loop = n / 2;
|
||
//偏移数
|
||
int offset = 1;
|
||
//当前要添加的元素
|
||
int count = 1;
|
||
|
||
while(loop) {
|
||
int i = startX;
|
||
int j = startY;
|
||
//模拟上侧从左到右
|
||
for(; j < startY + n - offset; j++) {
|
||
ans[startX][j] = count++;
|
||
}
|
||
//模拟右侧从上到下
|
||
for(; i < startX + n - offset; i++) {
|
||
ans[i][j] = count++;
|
||
}
|
||
//模拟下侧从右到左
|
||
for(; j > startY; j--) {
|
||
ans[i][j] = count++;
|
||
}
|
||
//模拟左侧从下到上
|
||
for(; i > startX; i--) {
|
||
ans[i][j] = count++;
|
||
}
|
||
//偏移值每次加2
|
||
offset+=2;
|
||
//遍历起始位置每次+1
|
||
startX++;
|
||
startY++;
|
||
loop--;
|
||
}
|
||
//若n为奇数需要单独给矩阵中间赋值
|
||
if(n%2)
|
||
ans[mid][mid] = count;
|
||
|
||
return ans;
|
||
}
|
||
```
|
||
Scala:
|
||
```scala
|
||
object Solution {
|
||
def generateMatrix(n: Int): Array[Array[Int]] = {
|
||
var res = Array.ofDim[Int](n, n) // 定义一个n*n的二维矩阵
|
||
var num = 1 // 标志当前到了哪个数字
|
||
var i = 0 // 横坐标
|
||
var j = 0 // 竖坐标
|
||
|
||
while (num <= n * n) {
|
||
// 向右：当j不越界，并且下一个要填的数字是空白时
|
||
while (j < n && res(i)(j) == 0) {
|
||
res(i)(j) = num // 当前坐标等于num
|
||
num += 1 // num++
|
||
j += 1 // 竖坐标+1
|
||
}
|
||
i += 1 // 下移一行
|
||
j -= 1 // 左移一列
|
||
|
||
// 剩下的都同上
|
||
|
||
// 向下
|
||
while (i < n && res(i)(j) == 0) {
|
||
res(i)(j) = num
|
||
num += 1
|
||
i += 1
|
||
}
|
||
i -= 1
|
||
j -= 1
|
||
|
||
// 向左
|
||
while (j >= 0 && res(i)(j) == 0) {
|
||
res(i)(j) = num
|
||
num += 1
|
||
j -= 1
|
||
}
|
||
i -= 1
|
||
j += 1
|
||
|
||
// 向上
|
||
while (i >= 0 && res(i)(j) == 0) {
|
||
res(i)(j) = num
|
||
num += 1
|
||
i -= 1
|
||
}
|
||
i += 1
|
||
j += 1
|
||
}
|
||
res
|
||
}
|
||
}
|
||
```
|
||
C#：
|
||
```csharp
|
||
public class Solution {
|
||
public int[][] GenerateMatrix(int n) {
|
||
int[][] answer = new int[n][];
|
||
for(int i = 0; i < n; i++)
|
||
answer[i] = new int[n];
|
||
int start = 0;
|
||
int end = n - 1;
|
||
int tmp = 1;
|
||
while(tmp < n * n)
|
||
{
|
||
for(int i = start; i < end; i++) answer[start][i] = tmp++;
|
||
for(int i = start; i < end; i++) answer[i][end] = tmp++;
|
||
for(int i = end; i > start; i--) answer[end][i] = tmp++;
|
||
for(int i = end; i > start; i--) answer[i][start] = tmp++;
|
||
start++;
|
||
end--;
|
||
}
|
||
if(n % 2 == 1) answer[n / 2][n / 2] = tmp;
|
||
return answer;
|
||
}
|
||
}
|
||
```
|
||
|
||
<p align="center">
|
||
<a href="https://programmercarl.com/other/kstar.html" target="_blank">
|
||
<img src="../pics/网站星球宣传海报.jpg" width="1000"/>
|
||
</a>
|