Homework problem N on Fibonacci Heaps

Due Nov 6.

Fibonacci Heaps

Questions designed to explore the operations on Fibonacci heaps in some detail.

  1. (7 points) Prove (by argument) or disprove (by counterexample sequence of constructing steps): If a tree in a fibonacci heap has no marked nodes, then the number of nodes in the tree is a power of 2 (like a binomial tree).

    Hint: regardless whether trying to prove or disprove, it is helpful to think about the idea of a minimal counterexample.

  2. (3 points) The converse is definitely not true. A fibonacci tree may have some marked nodes and still have size which is a power of two.

    Give a sequence of fibonacci heap function calls that results in a heap consisting of just one tree, containing just one node, which is marked.