[每日 LeetCode] 766. Toeplitz Matrix

Description:

A matrix is Toeplitz if every diagonal from top-left to bottom-right has the same element.

Now given an M x N matrix, return True  if and only if the matrix is Toeplitz .
 

Example 1:

Input: matrix = [
  [1,2,3,4],
  [5,1,2,3],
  [9,5,1,2]
]
Output: True
Explanation:
In the above grid, the diagonals are:
"[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]".
In each diagonal all elements are the same, so the answer is True.
​

Example 2:

Input: matrix = [
  [1,2],
  [2,2]
]
Output: False
Explanation:
The diagonal "[1, 2]" has different elements.
​

Note:

1. matrix will be a 2D array of integers.
2. matrix will have a number of rows and columns in range [1, 20].
3. matrix[i][j] will be integers in range [0, 99] .

Follow up:

1. What if the matrix is stored on disk, and the memory is limited such that you can only load at most one row of the matrix into the memory at once?
2. What if the matrix is so large that you can only load up a partial row into the memory at once?

思路：本题要求判断二维矩阵是否为 Toeplitz 矩阵，该矩阵的特点为斜右方的数字相等，且该矩阵有可能不是方阵。依次遍历数组，判断每个元素的值是否等于右下方的值，若不等则立即返回 false，否则返回 true。

C++ 代码

class Solution {
public:
    bool isToeplitzMatrix(vector<vector<int>>& matrix) {
        for (int i = 0; i < matrix.size() - 1; ++i) {
            for (int j = 0; j < matrix[i].size() - 1; ++j) {
                if (matrix[i][j] != matrix[i + 1][j + 1]) 
                    return false;
            }
        }
        return true;
    }
};
​

运行时间：24ms

运行内存：9.6M