Homework N Model Solution

 

Note that node[x] implies a node with key[x].

 

a.         The statement can be disproved by the following sequence:

            

            Fib-Heap-Insert(H, node[1])

            Fib-Heap-Insert(H, node[2])

            Fib-Heap-Insert(H, node[3])

            Fib-Heap-Insert(H, node[4])

            Fib-Heap-Insert(H, node[5)]

            Fib-Heap-Extract-Min(H)

            Fib-Heap-Decrease-Key(H, node[3], 1)

 

            The above sequence creates the following heap:

 

                         2 - 1

                        /

                      4

                      |

                      5

 

            The tree with root node[2] contains 3 nodes (which is not a
power of 2), none of which are marked.

 

 

b.         Fib-Heap-Insert(H, node[1])

            Fib-Heap-Insert(H, node[2])

            Fib-Heap-Insert(H, node[3])

            Fib-Heap-Insert(H, node[4])

            Fib-Heap-Insert(H, node[5)]

            Fib-Heap-Extract-Min(H)

            Fib-Heap-Delete(H, node[5])

            Fib-Heap-Extract-Min(H)

            Fib-Heap-Extract-Min(H)

 

            The above sequence creates a heap with a single tree whose only
node is node[4].  This node is marked.