生成螺旋矩阵（方阵、矩阵）

54. Spiral Matrix

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Submissions: 250811 Difficulty: Medium

Given a matrix of m x n elements (m rows, n columns), return all elements of the matrix in spiral order.
For example,

Given the following matrix:
[

[ 1, 2, 3 ],

[ 4, 5, 6 ],

[ 7, 8, 9 ]

]
You should return 

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

.

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方法：

（1）从外环开始，每次生成矩阵的一个环数据

（2）然后更新环的起点和大小（行数和列数）

vector<vector<int>> generateMatrix(int m, int n) {
vector<vector<int>> res(m, vector<int>(n));

int num_row = m, row_start = 0;
int num_col = n, col_start = 0;
int k = 1;

while (num_row > 0 && num_col > 0) {
//上边
for (int i = 0; i < num_col; ++i)
res[row_start][col_start + i] = k++;

//右边
for (int i = 1; i < num_row; ++i)
res[row_start + i][col_start + num_col - 1] = k++;

//下边,因为第一个 for 已经至少遍历了上边一行，若 num_row > 1 才可能执行本 for 循环
for (int i = num_col - 2; i >= 0 && num_row > 1; --i)
res[row_start + num_row - 1][col_start + i] = k++;

//左边,因为第二个 for 已经至少遍历了右边一列，若 num_col > 1 才可能执行本 for 循环
for (int i = num_row - 2; i >= 1 && num_col > 1; --i)
res[row_start + i][col_start] = k++;

//缩小一个单位的外环
num_row -= 2;
num_col -= 2;
++row_start;
++col_start;
}

return res;
}