leetcode59-Spiral Matrix II(生成蛇形矩阵)

问题描述：

Given an integer n, generate a square matrix filled with elements from 1 to n2 in spiral order.

For example,
Given n = 3,

You should return the following matrix:

[
 [ 1, 2, 3 ],
 [ 8, 9, 4 ],
 [ 7, 6, 5 ]
]

问题求解：

class Solution {
public:
    vector<vector<int>> generateMatrix(int n) {
        //关键是要找到(x1,y1)，(x2,y2)的位置，则上下左右的边界即可确定！！！
        if(n <= 0) return {};
        vector<vector<int>> matrix(n,vector<int>(n,0));//！！！
        //(x1,y1)表示遍历每一圈左上角元素的位置(0,0),(1,1)...！！！
        int x1=0, y1=0;
        int index=1;
        int cnt=n*n;
        while(index <= cnt)
        {//一共有cnt个位置需要赋值
            //(x2,y2)表示遍历每一圈右下角元素的位置(n-1,n-1),(n-2,n-2)...！！！
            int x2=n-1-x1;
            int y2=n-1-y1;
            for(int i=y1;i<=y2&&index<=cnt;i++)
            {//从左到右
                matrix[x1][i] = index;
                index++;
            }
            for(int i=x1+1;i<x2&&index<=cnt;i++)
            {//从上到下(不包括上界和下界)
                matrix[i][y2] = index;
                index++;
            }
            for(int i=y2;i>=y1&&index<=cnt;i--)
            {//从右到左
                matrix[x2][i] = index;
                index++;
            }
            for(int i=x2-1;i>x1&&index<=cnt;i--)
            {//从下到上(不包括上界和下界)
                matrix[i][y1] = index;
                index++;
            }
            x1++;y1++;
        }
        return matrix;
    }
};

方法二：

class Solution {
public:
    vector<vector<int> > generateMatrix(int n) {
            vector<vector<int> > matrix(n,vector<int>(n,0));
            if(n <= 0) return matrix;
            int cnt = n * n;
            int index = 1;
            int beginX = 0,endX = n - 1;
            int beginY = 0,endY = n - 1;
            while(index <= cnt){
                //(1)从左到右
                for(int i = beginY;i <= endY;++i){
                    matrix[beginX][i] = index;
                    ++index;
                }
                ++beginX;//从左到右结束后左上角元素横坐标加1
                //(2)从上到下
                for(int i = beginX;i <= endX;++i){
                    matrix[i][endY] = index;
                    ++index;
                }
                --endY;//从上到下结束后右下角元素纵坐标减1
                //(3)从右到左
                for(int i = endY;i >= beginY;--i){
                    matrix[endX][i] = index;
                    ++index;
                }
                --endX;//从右到左结束后右下角元素横坐标减1
                //(4)从下到上
                for(int i = endX;i >= beginX;--i){
                    matrix[i][beginY] = index;
                    ++index;
                }
                ++beginY;//从下到上结束后左上角元素纵坐标加1
            }
            return matrix;
        }
};