Please help with Python Code:::

$1.$ ford fulkerson:

$-$ Guide:

$-$ Ford$-$Fulkerson works by repeatedly sending flow along paths from source to sink$,$ updating the capacities of forward and backward edges accordingly.

$-$ Pseudocode:

FUNCTION ford fulkerson$($graph$,$ source, sink$)$ SET flow TO $0$ SET parent TO ARRAY OF SIZE length$($graph$)$ INITIALIZED WITH $-1$

WHILE bfs$($graph$,$ source, sink, parent$)$ RETURNS TRUE

SET path flow TO INFINITY

$//$ Find minimum flow in the found path

SET s TO sink

WHILE s IS NOT EQUAL TO source

SET path flow TO MINIMUM of path flow AND graph$[$parent$[$s$]][$s$]$

SET s TO parent$[$s$]$

$//$ Update residual capacities and reverse edges

SET v TO sink

WHILE v IS NOT EQUAL TO source

SET u TO parent $[$v$]$

DECREASE graph$[$u$][$v$]$ BY path flow

INCREASE graph$[$v$][$u$]$ BY path flow

SET v TO parent$[$v$]$

INCREASE flow BY path flow

RETURN flow

FUNCTION bfs $($graph$,$ source, sink, parent$)$ SET visited TO ARRAY OF SIZE length$($graph$)$ INITIALIZED WITH FALSE SET queue TO ARRAY CONTAINING source SET visited$[$source$]$ TO TRUE

WHILE queue IS NOT EMPTY

SET u TO first element in queue

REMOVE u from queue

FOR EACH index i AND value val in graph$[$u$]$

IF visited$[$i$]$ IS FALSE AND val $>0$

ADD i TO queue

SET visited$[$i$]$ TO TRUE

SET parent$[$i$]$ TO u

RETURN visited$[$sink$]$