Toeplitz-Matrix

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题目地址

LeetCode#766 Toeplitz Matrix

题目描述

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:

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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:

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Input: matrix = [[1,2],[2,2]]
Output: False
Explanation:
The diagonal "[1, 2]" has different elements.

Note:

  1. matrix will be a 2D array of integers.
  2. matrix will have a number of rows and columns in range [1, 20].
  3. matrix[i][j] will be integers in range [0, 99].

解题思路

  题目要求判断一个N x M的矩阵是否满足在一个斜线（斜线是从左上到右下）上的数字都相同的条件，直接按照题目要求进行判断就是了。

解题代码【.CPP】

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class Solution {
    bool Judge(vector<vector<int>> &matrix, int i, int j) {
        for (int x = i, y = j; x < matrix.size() && y < matrix[i].size(); ++x, ++y) {
            if (matrix[x][y] != matrix[i][j]) return false;
        }
        return true;
    }

public:
    bool isToeplitzMatrix(vector<vector<int>> &matrix) {
        if (matrix.empty()) return true;
        bool ret = true;
        for (int i = 0; i < matrix.size(); ++i) {
            if (!Judge(matrix, i, 0)) return false;
        }
        for (int j = 1; j < matrix[0].size(); ++j) {
            if (!Judge(matrix, 0, j)) return false;
        }
        return ret;
    }
};
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