[leetcode] 766. Toeplitz Matrix @ python

最新推荐文章于 2023-04-05 08:00:00 发布

原创最新推荐文章于 2023-04-05 08:00:00 发布 · 211 阅读

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本文介绍了一种特殊矩阵——Toeplitz矩阵，并提供了两种方法来判断一个给定的矩阵是否为Toeplitz矩阵。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。通过遍历矩阵的对角线或直接比较相邻元素的方法，可以有效地验证这一特性。

原题

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?

解法1

先从左到右, 再从上到下遍历matrix的对角线, 将对角线的元素放入集合里, 检查集合的长度是否大于1.

代码

class Solution(object):
    def isToeplitzMatrix(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: bool
        """
        row, col = len(matrix), len(matrix[0])
        # check from left to right
        for y in range(col):
            diag  = set()
            x = 0
            diag.add(matrix[x][y])
            while x+1 < row and y+1 < col:
                x += 1
                y += 1
                diag.add(matrix[x][y])
                # check
                if len(diag) > 1:
                    return False
        # check from up to down
        for x in range(1, row):
            diag = set()
            y = 0
            diag.add(matrix[x][y])
            while x+1 < row and y+1 < col:
                x += 1
                y += 1
                diag.add(matrix[x][y])
                # check
                if len(diag) > 1:
                    return False
        return True

解法2

直接遍历matrix, 如果发现某个元素与它的对角线元素不相等, 返回False.

代码

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