#Please do not post homework
#Ravali Bommanaboina, 12/6/20, Assignment 23
#Question 1
#{{1, 5}, {2, 6}, {2, 11}, {3, 10}, {4, 9}, {4, 13}, {5, 11}, {6, 7}, {6, 10}, {7, 13}, {8, 12}, {8, 14}, {11, 12}}
#[5, 10, 11, 4, 13, 6, 7, 6, 2, 11, 12, 8]
#Question 2
#[5, 10, 11, 2, 2, 4, 8, 11, 3, 9, 10, 13, 12, 13, 14]
#{{1, 5}, {2, 4}, {2, 5}, {2, 10}, {3, 9}, {3, 11}, {4, 6}, {7, 8}, {8, 11}, {9, 10}, {10, 13}, {12, 13}, {13, 14}, {14, 15}}, [11, 12]

#Question 3
#InvPruffer(Pruffer(T))=T

#Question 4
RandTree1:=proc(n) local f:
f:=RandF(n-2):
InvPruffer(f):
end:

#time(RandTree(2000)); is faster than time(RandTree1(2000)); this is because Joyal(f) uses a direct mapping
#add(seq(time(RandTree(2000)), i = 0 .. 20))/20;
#                          0.2964500000

#add(seq(time(RandTree1(2000)), i = 0 .. 20))/20;
#                          2.055050000

#Question 5
EstAveLeaves:=proc(n,K) local i:
(add(seq(nops(Leaves(RandTree(n))),i=1..K)))/K;
end:

#3733/100 is close to 99/exp(1)

#Question 6
R:=proc(e,b):
b*(b+e)^(e-1);
end: