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.
Input: matrix = [[1,2,3,4],[5,1,2,3],[9,5,1,2]]
In the above grid, the diagonals are "", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "", and in each diagonal all elements are the same, so the answer is True.
Input: matrix = [[1,2],[2,2]]
The diagonal "[1, 2]" has different elements.
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].
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.length == 0 return true if input.length == 1 or input.length ==1 (0..input.length-2).each do |i| (0..input.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.
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