题目

原题地址

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].

答题

思路一

1234
5123
9512

多维数组中

• 1元素的下标为 00、11、22
• 5元素的下标为 10、21
• 2元素的下标为 01、12、23
• 3元素的下标为 02、13

规律我想大家都明白了。

public boolean isToeplitzMatrix(int[][] matrix) {
    int xSize = matrix.length;
    if (xSize <= 1) {
        return true;
    }
    int[] temp = matrix[0];
    int ySize = temp.length;
    if (ySize <= 1) {
        return true;
    }
    boolean result = true;
    for (int x = 0; x < xSize - 1; x++) {
        result = result & check(matrix, x, 0, xSize, ySize);
        if (!result) {
             return false;
        }
    }
    for (int y = 0; y < ySize - 1; y++) {
        result = result & check(matrix, 0, y, xSize, ySize);
        if (!result) {
             return false;
        }
    }
    return true;
}

private boolean check(int[][] matrix, int x, int y, int xSize, int ySize) {
    if (x > xSize - 1 || y > ySize - 1) {
        return true;
    }
    if (x != 0 && y != 0) {
        if (matrix[x][y] != matrix[x - 1][y - 1]) {
            return false;
        }
    }
    return check(matrix, x + 1, y + 1, xSize, ySize);
}

再精简代码

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

思路二

1234
5123
9512

继续寻找规律，我们发现 9 和 4是不需要比较的，那么我们去掉这两个数：

123
5123
 512

第一行与最后一行的数组大小比其他行小1，且第一行元素等于第二行除去第一个元素的其他元素，以此类推。

public boolean isToeplitzMatrix(int[][] matrix) {
    int m = matrix.length, n = matrix[0].length;
    for (int i = 0; i < m - 1; i++) {
        int[] arr1 = Arrays.copyOfRange(matrix[i], 0, n - 1), arr2 = Arrays.copyOfRange(matrix[i + 1], 1, n);
        if (Arrays.equals(arr1, arr2)) {
            continue;
        } else
            return false;
    }
    return true;
}