[LintCode] Toeplitz Matrix

最新推荐文章于 2022-05-26 08:37:39 发布

转载最新推荐文章于 2022-05-26 08:37:39 发布 · 82 阅读

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原文链接：https://segmentfault.com/a/1190000015286530

本文介绍了一种简单高效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条对角线上的元素是否完全相同。通过遍历矩阵并比较相邻元素的方式实现。

Problem

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

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.

Solution

public class Solution {
    /**
     * @param matrix: the given matrix
     * @return: True if and only if the matrix is Toeplitz
     */
    public boolean isToeplitzMatrix(int[][] matrix) {
        // Write your code here
        // DP? No.
        // New arrays? No.
        // Why? Because it's too simple.
        int m = matrix.length;
        int n = matrix[0].length;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 || j == 0) continue;
                if (matrix[i][j] != matrix[i-1][j-1]) return false;
            }
        }
        return true;
    }
}