takes the graph matrix and a starting vertex as input. The function returns

information about the detected cycle: its length and the vertex where the cycle

begins. For graphs with no cycles, the function returns null $($in Java$)$ or None

$($in Python$).$ The input matrix must be square, with dimensions nxxn where n

is the number of nodes in the graph. Each entry graph$[$i$][$j$]$ should be $1$ if there

is a direct edge from node i to node j $,$ and $0$ otherwise. please help me in python, thank you. $```$

def floyd$($graph$,$ start$)$:

$"\text{'}!"$

Function to detect a cycle in a directed graph using Floyd's cycle finding algorithm.

Also known as the "tortoise and hare" algorithm.

:param graph: A $2$D list representing the adjacency matrix of the graph.

graph$[$i$][$j$]$ is $1$ if there is a direct edge from node i to node j$,$ otherwise $0.$

:param start: The starting vertex for cycle detection.

:return: A tuple of $($cycle$\_$length, cycle$\_$start$)$ if a cycle is found,

where cycle$\_$length is the length of the cycle and cycle$\_$start is the starting vertex of the cycle.

Returns None if no cycle is found.

Example:

For graph$4$:

$[$

$[0,1,0,0],$ # Node $0->$ Node $1$

$[0,0,1,0],$ # Node $1->$ Node $2$

$[0,0,0,1],$ # Node $2->$ Node $3$

$[1,0,0,0]$ # Node $3->$ Node $0($completing the cycle$)$

$]$

$"!",$

# TODO: Implement Floyd's cycle finding algorithm

# Hint: Use two pointers $($tortoise and hare$)$ moving at different speeds

return None

$```$