Commute Time Matrix Property Check

Problem

Verify that a matrix is a valid commute time matrix.

A commute time matrix must be square with zero diagonal, non-negative entries, and perfect symmetry (C[i][j] equals C[j][i]). Return True when all of these hold. matrix is a list of n lists of numbers.

Hint

Commute time is symmetric even on directed graphs because it uses the underlying walk.

Test cases

case 1

in: [[[0,4,8],[4,0,4],[8,4,0]]]

expected: true

case 2

in: [[[0,4],[5,0]]]

expected: false

case 3

in: [[[1,2],[2,0]]]

expected: false

case 4

in: [[[0,-1],[-1,0]]]

expected: false

case 5

in: [[[0]]]

expected: true

Starter codePython

def commute_time_symmetric(matrix):
    # Your code here
    pass

5 test cases · run your code against them in the editor