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# Name:Treasa Bency Biju Jose
# Date: 12-04-2020
# Assignment #23
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1. RandTree(14);
 {{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}}


Pruffer(%);
           [5, 10, 11, 4, 13, 6, 7, 6, 2, 11, 12, 8]

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2. f := RandF(15);
  f := [2, 11, 15, 8, 10, 14, 12, 9, 13, 11, 1, 6, 13, 14, 7]

Joyal(f);
{{1, 11}, {1, 13}, {2, 11}, {3, 15}, {4, 8}, {5, 10}, {6, 12}, 

  {6, 14}, {7, 12}, {7, 15}, {8, 9}, {9, 13}, {10, 11}, {13, 14}}, 

  [2, 14]

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3. t := RandTree(100);
evalb(InvPruffer(Pruffer(t)) = t);
                              true

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4. 
RandTree1 := proc(n) local f; 
InvPruffer(Pruffer(RandTree(n))); 
end proc;

time(RandTree(200));
                             0.015

time(RandTree1(200));
                             1.468

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5. 
EstAveLeaves := proc(n, K) local ave, T, i; 
ave := 0; 
for i to K do 
T := RandTree(n); 
ave := ave + nops(Leaves(T)); 
end do; 
ave := evalf(ave/K); 
end proc;

EstAveLeaves(100, 1000);
                          37.32000000

EstAveLeaves(100, 1000);
                          37.35200000

evalf(99/exp(1));
                          36.42006468

EstAveLeaves(100, 1000);
                          37.52100000

EstAveLeaves(100, 1000);
                          37.28900000

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