#OK to post homework
#Ravali Bommanaboina, 11/15/20, Assignment 18
#Question 1
AllKComponentsGraphs:=proc(n,K) local S,s,C:
S:=AllGraphs(n):
C:={}:

for s in S do
 if nops(CCs(s))=K then
  C:=C union {s}:
 fi:
od:

C:
end:

NuKcomponentsGraphs:=proc(n,K) local i,C:
C:=[]:

for i from 1 to n do
  C:=[op(C),nops(AllKComponentsGraphs(i,K))]:
od:

C:
end:
#NuKcomponentsGraphs(5,2); -> [0,1,3,19,230]
#A323875
#NuKcomponentsGraphs(5,3); -> [0,0,1,6,55]
#A323876

#Question 2
AveNuCC:=proc(n,K,M) local i,S:
S:=[]:
for i from 1 to M do
	S:=[op(S),nops(CCs(RandGr(n,K)))]:
od:
Statistics[Mean](S):
end:

#Question 3
EstimateCutOff:=proc(n,M) local i,k,ave:
ave:=2:
k:=1:
while(ave>=1.05) do
ave:=AveNuCC(n,k,M):
k:=k+1:
od:
k:
end: