566. Reshape the Matrix

问题描述

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

题目链接：

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思路分析

实现MATLAB方法，将一个矩阵的形状改变，即行数和列数变化，但是元素不变。如果不能变化就返回原来的矩阵。

矩阵能够变化的前提是元素的数量是一致的，所以首先判断能否变化。然后，元素在新矩阵中的位置就是它当前序号（假设一字排开）除新矩阵的列数的到行号，模除新矩阵的列数得到列号。

代码

class Solution {
public:
    vector<vector<int>> matrixReshape(vector<vector<int>>& nums, int r, int c) {
        int row = nums.size();
        int column = nums[0].size();
        if (row * column != r * c) 
            return nums;
        vector<vector<int>> result(r, vector<int>(c, 0));
        for (int i = 0; i < row; i++){
            for (int j = 0; j < column; j++){
                int k = i * column + j;
                result[k / c][k % c] = nums[i][j];
            }
        }
        return result;
    }
};

时间复杂度：$O(n)$
空间复杂度：$O(n)$

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反思

vector赋值的方法，学到了，如何建立一个vector，设置它的长度和初始值。