LWC 68: 766. Toeplitz Matrix

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最新推荐文章于 2020-09-27 21:52:07 发布

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本文介绍了一种判断矩阵是否为Toeplitz矩阵的方法，并提供了Java和Python两种语言的实现代码。Toeplitz矩阵的特点是从左上到右下的每条对角线上的元素都相同。

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LWC 68: 766. Toeplitz Matrix

传送门：766. Toeplitz Matrix

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 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].

思路：
对角线遍历，注意对角线的性质：当前元素为matrix[i][j]，下一元素为matrix[i+1][j+1]。

代码如下：

    public boolean isToeplitzMatrix(int[][] matrix) {
        int n = matrix.length;
        int m = matrix[0].length;

        for (int j = 0; j < m; ++j) {
            int i = 0;
            while (i + 1 < n && j + 1 < m) {
                if (matrix[i + 1][j + 1] != matrix[i][j]) return false;
                i ++;
                j ++;
            }
        }

        for (int i = 0; i < n; ++i) {
            int j = 0;
            while (i + 1 < n && j + 1 < m) {
                if (matrix[i + 1][j + 1] != matrix[i][j]) return false;
                i ++;
                j ++;
            }
        }
        return true;
    }

当然你可以直接遍历，只要判断每个元素所在对角线的下一个元素是否与当前元素相等即可。

Java版本：

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

Python版本：

    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        n = len(matrix)
        m = len(matrix[0])

        for i in range(0, n - 1):
            for j in range(0, m - 1):
                if matrix[i][j] != matrix[i + 1][j + 1]: return False
        return True