What is the maximum flow of the network below from node $1$ to node $7?$

Answer must be number and Python algorithm you used to get that number.

Use it as an example to calculate the maximum flow $($add all edges$)$for the network in the photo.

class MaximumFlow:

def $\_\_$init$\_\_($self$,$ nodes$)$:

self.nodes $=$ nodes

self.graph $=\{\}$

for i in self.nodes:

for j in self.nodes:

self.graph$[($i$,$ j$)]=0$

def add$\_$edge$($self$,$ node$\_$a$,$ node$\_$b$,$ capacity$)$:

self.graph$[($node$\_$a$,$ node$\_$b$)]+=$ capacity

def add$\_$flow$($self$,$ node, sink, flow$)$:

if node in self.seen:

return $0$

self.seen.add$($node$)$

if node $==$ sink:

return flow

for next$\_$node in self.nodes:

if self.flow$[($node$,$ next$\_$node$)]>0$:

new$\_$flow $=$ min$($flow$,$ self.flow$[($node$,$ next$\_$node$)])$

inc $=$ self.add$\_$flow$($next$\_$node, sink, new$\_$flow$)$

if inc $>0$:

self.flow$[($node$,$ next$\_$node$)]-=$ inc

self.flow$[($next$\_$node, node$)]+=$ inc

return inc

return $0$

def construct$($self$,$ source, sink$)$:

self.flow $=$ self.graph.copy$()$

total $=0$

while True:

self.seen $=$ set$()$

add $=$ self.add$\_$flow$($source$,$ sink$,$ float$("$inf$"))$

if add $==0$:

break

total $+=$ add

return total

The algorithm can be used like this in the example network:

m $=$ MaximumFlow$([1,2,3,4,5])$

m$.$add$\_$edge$(1,2,4)$

m$.$add$\_$edge$(1,3,6)$

m$.$add$\_$edge$(2,3,8)$

m$.$add$\_$edge$(2,4,3)$

m$.$add$\_$edge$(3,5,4)$

m$.$add$\_$edge$(4,5,5)$

print$($m$.$construct$(1,5))$ # $7$