766. Toeplitz Matrix (leetcode)

最新推荐文章于 2021-02-22 10:23:43 发布

Valerie7012

最新推荐文章于 2021-02-22 10:23:43 发布

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分类专栏： leetcode 算法

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本文介绍了一种简单的方法来判断一个给定的矩阵是否为Toeplitz矩阵，即矩阵中从左上到右下的每一条对角线上的元素都相同。通过遍历矩阵并比较相邻元素，可以在O(row * col)的时间复杂度内完成验证。

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Toeplitz Matrix

Toeplitz Matrix
- 题目
- 解决

题目

leetcode题目

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:

1234
5123
9512

In the above grid, the diagonals are "[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]", and 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:

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

解决

时间复杂度为O(row * col)
空间复杂度为O(1)

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