566. Reshape the Matrix

In MATLAB, there is a very useful function called 'reshape', which can reshape a matrix into a new one with different size but keep its original data.

You're given a matrix represented by a two-dimensional array, and two positive integers r and c representing the row number and column number of the wanted reshaped matrix, respectively.

The reshaped matrix need to be filled with all the elements of the original matrix in the same row-traversing order as they were.

If the 'reshape' operation with given parameters is possible and legal, output the new reshaped matrix; Otherwise, output the original matrix.

Example 1:

Input: 
nums = 
[[1,2],
 [3,4]]
r = 1, c = 4
Output: 
[[1,2,3,4]]
Explanation:
The row-traversing of nums is [1,2,3,4]. The new reshaped matrix is a 1 * 4 matrix, fill it row by row by using the previous list.

Example 2:

Input: 
nums = 
[[1,2],
 [3,4]]
r = 2, c = 4
Output: 
[[1,2],
 [3,4]]
Explanation:
There is no way to reshape a 2 * 2 matrix to a 2 * 4 matrix. So output the original matrix.

Note:
The height and width of the given matrix is in range [1, 100].
The given r and c are all positive.

思路:主要还是坐标变换,不管是mn还是rc的矩阵,其展开成一维的数组时都有对应的唯一坐标转换映射.可以理解为先将mn矩阵映射到一维,再从一维映射到rc,找好映射关系即可.
还有要注意的就是嵌套vector的初始化,没想到还能这么玩.

class Solution {
public:
    vector<vector<int>> matrixReshape(vector<vector<int>>& nums, int r, int c) {
        int m = nums.size(); // // 原矩阵的行数
        int n = nums[0].size(); // 原矩阵的列数
        if (r*c != m*n) return nums;
        vector<vector<int>> result(r, vector<int>(c)); // 嵌套vector初始化
        for (int i = 0; i < r*c; i++) {
            result[i/c][i%c] = nums[i/n][i%n]; // 坐标转换
        }
        return result;
    }
};