Toeplitz Matrix - LeetCode

Posted 2020-11-02 chenqingyun

LeetCode 题目地址

描述

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].

题目意思就是如果一个矩阵的每一方向由左上到右下的对角线上具有相同元素，那么这个矩阵是托普利茨矩阵。

给定一个 M x N 的矩阵，当且仅当它是托普利茨矩阵时返回 True。

解法

根据给定的例子可以这样分析，左上到右下的对角线上的元素相同，比如1数字，位置分别是 matrix[0][0]，matrix[1][1]，matrix[2][2]，比如2数字，位置分别是matrix[0][1]，matrix[1][2]，matrix[2][3]，所以可以得出一个结论，满足matrix[i][j] == matrix[i+1][j+1]就是托普利茨矩阵。这样就很简单啦，两层 for 循环搞定。

代码如下：

public boolean isToeplitzMatrix(int[][] matrix) {
    for(int i=0; i<matrix.length-1;i++){
        for(int j=0; j<matrix[i].length-1; j++){
            if(matrix[i][j] != matrix[i+1][j+1]){
                return false;
            }
        }
    }
    return true;
}