766. Toeplitz Matrix

最新推荐文章于 2021-01-11 15:21:41 发布

转载最新推荐文章于 2021-01-11 15:21:41 发布 · 185 阅读

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原文链接：http://www.cnblogs.com/bernieloveslife/p/9801104.html

本文介绍了一种算法，用于判断一个给定的二维矩阵是否为Toeplitz矩阵，即每一条从左上到右下的对角线上元素是否相同。通过遍历矩阵的每个元素并与前一元素比较，实现高效判断。

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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:

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].

Follow up:

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?
What if the matrix is so large that you can only load up a partial row into the memory at once?

class Solution:
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        if len(matrix)==0:
            return True
        for i in range(1,len(matrix)):
            for j in range(1,len(matrix[0])):
                if matrix[i][j]!=matrix[i-1][j-1]:
                    return False
        return True

转载于:https://www.cnblogs.com/bernieloveslife/p/9801104.html