CMPS 201 Third Homework, Fall 04
3 problems, 30 pts, Due Tuesday, October 19
1. (10 pts) Problem 7-3 on page 161 (stooge sort).
2. (10 pts) Use an information theoretic (decision tree) argument to show that at least
2n−o(n) comparisons are required to merge two sorted lists Aand Beach containing
nelements. (Hint: First, get a good lower bound on the number of ways that two
n-element lists with distinct elements can be merged, you may need to approximate a
binomial coefficient.)
3. (10 pts) The total depth of the leaves in a tree is the sum over the leaves of the depth
of the leaf. Use induction to show that the total depth of every full binary tree T is at
least `(T) log `(T) where `(T) is the number of leaves in T. (Hint: In the inductive step,
find the two subtrees of Tand applying the inductive hypotheses to these trees to get a
lower bound in terms of how many internal nodes are on the left side. Then use calculus
to minimize this bound and underestimate the total depth of the leaves).
0