1) Please look at the program http://www.cs.rpi.edu/~moorthy/Courses/CSCI2300/Graph2015-6-1.cc

2) Please look at the program http://www.cs.rpi.edu/~moorthy/Courses/CSCI2300/Graph2015-6-2.cc

3) Using the formula m (number of bits needed in the bloom filter) and p(.01) is the false positive -n*ln(p)/(ln(2)^2
1630000 bits and the number of hash functions is m/n*ln(2) = 6

3) Tree edges are for 16 prufer sequences:
2-1,3-1,1-4; 3-1,1-2,2-4; 2-1,1-3,3-4; 2-1,2-4,4-3;
3-2,2-1,1-4; 1-2,3-2,2-4; 1-2,2-3,3-4; 1-2,2-4,4-3;
2-3,3-1,1-4; 1-3,3-2,2-4; 1-3,2-3,3-4; 1-3,2-4,3-4;
2-4,3-1,1-4; 1-4,3-2,2-4; 1-4,2-3,3-4; 1-4,2-4,3-4;