題目描述：

Given a matrix A, return the transpose of A.

The transpose of a matrix is the matrix flipped over it‘s main diagonal, switching the row and column indices of the matrix.

Example 1:

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

Example 2:

Input: [[1,2,3],[4,5,6]]
Output: [[1,4],[2,5],[3,6]]
 

Note:

1. 1 <= A.length <= 1000
2. 1 <= A[0].length <= 1000

解題思路：

暴力遍歷原來矩陣的每個元素，放到輸出矩陣的對應位置。

由於veector的內存分配機制，由於已知輸出矩陣的大小，所以在每個vector定義時指定空間大小會節省運行時間。

代碼：

 1 class Solution {
 2 public:
 3     vector<vector<int>> transpose(vector<vector<int>>& A) {
 4         vector<vector<int
 
> > res;
 5         res.reserve(A[0].size());
 6         for (int i = 0; i < A[0].size(); ++i) {
 7             vector<int> tmp;
 8             tmp.reserve(A.size());
 9             for (int j = 0; j < A.size(); ++j) {
10                 tmp.push_back(A[j][i]);
11             }
12             res.push_back(tmp);
 
13         }
14         return res;
15     }
16 };

867. Transpose Matrix