766. Toeplitz Matrix

QUESTION:

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:

  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].

EXPLANATION:

看到这个题目的想法就是按照顺序来呗,分成横向和竖向两种。

1.首先处理横向的情况:横向的时候就进行遍历操作,对j进行遍历,然后进行判断,这样就可以了。

2.进行竖向操作的时候,只需要进行一次斜的遍历,这样就可以避免重复操作了。

如图:

第一步:

x,x,x,x,x,x

o,x,x,x,x,x

o,o,x,x,x,x

o,o,o,x,x,x

o,o,o,o,x,x

o,o,o,o,o,x

第二步:

x,x,x,x,x,x

x,x,x,x,x,x

o,x,x,x,x,x

o,o,x,x,x,x

o,o,o,x,x,x

o,o,o,o,x,x

第三步:

x,x,x,x,x,x

x,x,x,x,x,x

x,x,x,x,x,x

o,x,x,x,x,x

o,o,x,x,x,x

o,o,o,x,x,x

SOLUTION:

class Solution {
    public boolean isToeplitzMatrix(int[][] matrix) {
        for(int i = 0;i<matrix.length;i++){
            if(i==0){
                for(int j = 0;j<matrix[i].length;j++){
                    int m = 0;int n=j;
                    int tmp = matrix[m][n];
                    while (m<matrix.length&&n<matrix[m].length){
                        if(matrix[m][n]!=tmp) return false;
                        m++;n++;
                    }
                }
            }else{
                int m = i;int n=0;
                int tmp = matrix[m][n];
                while (m<matrix.length&&n<matrix[m].length){
                    if(matrix[m][n]!=tmp) return false;
                    m++;n++;
                }
            }
        }
        return true;
    }
}