Please consider my code in the picture and help with the following code $($only the #your code here$)$ and pass the testing.

class UndirectedGraph:

# n is the number of vertices

# we will label the vertices from $0$ to self.n $-1$

# We simply store the edges in a list.

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

assert n $>=1,$ 'You are creating an empty graph $--$ disallowed'

self.n $=$ n

self.edges $=[]$

self.vertex$\_$data $=[$None$]*$self$.$n

def set$\_$vertex$\_$data$($self$,$ j$,$ dat$)$:

assert j $$ self.n

self.vertex$\_$data$[$j$]=$ dat

def get$\_$vertex$\_$data$($self$,$ j$)$:

assert j $$ self.n

return self.vertex$\_$data$[$j$]$

def add$\_$edge$($self$,$ i$,$ j$,$ wij$)$:

assert i $$ self.n

assert j $$ self.n

assert i $!=$ j

# Make sure to add edge from i to j with weight wij

self.edges.append$(($i$,$ j$,$ wij$))$

def sort$\_$edges$($self$)$:

# sort edges in ascending order of weights.

self.edges $=$ sorted$($self$.$edges, key$=$lambda edg$\_$data: edg$\_$data$[2])$

$2$A: compute scc

def compute$\_$scc$($g$,$ W$)$:

# create a disjoint forest with as many elements as number of vertices

# Next compute the strongly connected components using the disjoint forest data structure

d $=$ DisjointForests$($g$.$n$)$

# your code here

$**$Test$**$

g$3=$ UndirectedGraph$(8)$

g$3.$add$\_$edge$(0,1,0\mathrm{.}5)$

g$3.$add$\_$edge$(0,2,1\mathrm{.}0)$

g$3.$add$\_$edge$(0,4,0\mathrm{.}5)$

g$3.$add$\_$edge$(2,3,1\mathrm{.}5)$

g$3.$add$\_$edge$(2,4,2\mathrm{.}0)$

g$3.$add$\_$edge$(3,4,1\mathrm{.}5)$

g$3.$add$\_$edge$(5,6,2\mathrm{.}0)$

g$3.$add$\_$edge$(5,7,2\mathrm{.}0)$

res $=$ compute$\_$scc$($g$3,2\mathrm{.}0)$

print$(\text{'}$SCCs with threshold $2\mathrm{.}0$ computed by your code are:$\text{'})$

assert len$($res$)==2,$ f'Expected $2$ SCCs but got $\{$len$($res$)\}\text{'}$

for $($k$,$ s$)$ in res.items$()$:

print$($s$)$

# Let us check that your code returns what we expect.

for $($k$,$ s$)$ in res.items$()$:

if $($k in $[0,1,2,3,4])$:

assert $($s $==$ set$([0,1,2,3,4])),\text{'}\{0,1,2,3,4\}$ should be an SCC$\text{'}$

if $($k in $[5,6,7])$:

assert $($s $==$ set$([5,6,7])),\text{'}\{5,6,7\}$ should be an SCC$\text{'}$

# Let us check that the thresholding works

print$(\text{'}$SCCs with threshold $1\mathrm{.}5\text{'})$

res$2=$ compute$\_$scc$($g$3,1\mathrm{.}5)$ # This cutsoff edges $2,4$ and $5,6,7$

for $($k$,$ s$)$ in res$2.$items$()$:

print$($s$)$

assert len$($res$2)==4,$ f'Expected $4$ SCCs but got $\{$len$($res$2)\}\text{'}$

for $($k$,$ s$)$ in res$2.$items$()$:

if k in $[0,1,2,3,4]$:

assert $($s $==$ set$([0,1,2,3,4])),\text{'}\{0,1,2,3,4\}$ should be an SCC$\text{'}$

if k in $[5]$:

assert s $==$ set$([5]),\text{'}\{5\}$ should be an SCC with just a single node.$\text{'}$

if k in $[6]$:

assert s $==$ set$([6]),\text{'}\{6\}$ should be an SCC with just a single node.$\text{'}$

if k in $[7]$:

assert s $==$ set$([7]),\text{'}\{7\}$ should be an SCC with just a single node.$\text{'}$

print$(\text{'}$All tests passed: $10$ points'$)$

$2$B:

def compute$\_$mst$($g$)$:

# return a tuple of two items

# $1.$ list of edges $($i$,$j$)$ that are part of the MST

# $2.$ sum of MST edge weights.

d $=$ DisjointForests$($g$.$n$)$

mst$\_$edges $=[]$

g$.$sort$\_$edges$()$

# your code here

$**$Test$**$

g$3=$ UndirectedGraph$(8)$

g$3.$add$\_$edge$(0,1,0\mathrm{.}5)$

g$3.$add$\_$edge$(0,2,1\mathrm{.}0)$

g$3.$add$\_$edge$(0,4,0\mathrm{.}5)$

g$3.$add$\_$edge$(2,3,1\mathrm{.}5)$

g$3.$add$\_$edge$(2,4,2\mathrm{.}0)$

g$3.$add$\_$edge$(3,4,1\mathrm{.}5)$

g$3.$add$\_$edge$(5,6,2\mathrm{.}0)$

g$3.$add$\_$edge$(5,7,2\mathrm{.}0)$

g$3.$add$\_$edge$(3,5,2\mathrm{.}0)$

$($mst$\_$edges, mst$\_$weight$)=$ compute$\_$mst$($g$3)$

print$(\text{'}$Your code computed MST: $\text{'})$

for $($i$,$j$,$wij$)$ in mst$\_$edges:

print$($f$\text{'}\backslash$t $\{($i$,$j$)\}$ weight $\{$wij$\}\text{'})$

print$($f$\text{'}$Total edge weight: $\{$mst$\_$weight$\}\text{'})$

assert mst$\_$weight $==9\mathrm{.}5,$ 'Optimal MST weight is expected to be $9\mathrm{.}5\text{'}$

assert $(0,1,0\mathrm{.}5)$ in mst$\_$edges

assert $(0,2,1\mathrm{.}0)$ in mst$\_$edges

assert $(0,4,0\mathrm{.}5)$ in mst$\_$edges

assert $(5,6,2\mathrm{.}0)$ in mst$\_$edges

assert $(5,7,2\mathrm{.}0)$ in mst$\_$edges

assert $(3,5,2\mathrm{.}0)$ in mst$\_$edges

assert $(2,3,1\mathrm{.}5)$ in mst$\_$edges or $(3,4,1\mathrm{.}5)$ in mst$\_$edges

print$(\text{'}$All tests passed: $10$ points!$\text{'})$