# TOEPLITZ MATRIX | MATRIX PROBLEMS | LEETCODE | INTERVIEW PRACTICE

By: Saurav

2018-03-16 03:38:00 UTC

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].

Leetcode

This problem looks hard but it is unless you are able to find out the pattern.

Yes, this is a pattern based problem. Best way to see it is to work through test cases. try writing the indexes of all diagonal elements on a piece of paper and then a pattern will come right in front of your eyes.

The pattern is that each element a[i][j] in the matrix should be equal to a[i+1][j+1] where i and j varies between 0 - m and 0 - n where m and n are a number of rows and columns.

Lets see the code:

```def toelitz(input)
return false if input.length == 0 or input[0].length == 0
return true if input.length == 1 or input[0].length ==1

(0..input.length-2).each do |i|
(0..input[0].length-2).each do |j|
return false if input[i][j] != input[i+1][j+1]
end
end

return true

end ```

These are few of those problems where you need to pay good attention and walk through a test case before coming up with an algo.