Problem L
Assigned Oct 16+5, due Nov 4.
Accelerated Binomial Heaps
- (9 points)
Construct a sequence of Binomial_Heap _Insert(), _Union(), and _Extract_Min()
calls, including at least one _Extract_Min() call, such that
the total number of Binomial_Link() calls made within the sequence
is smaller for acceleratedBinomialHeaps than for binomialHeaps.
For binomialHeap definitions use either CLR pseudocode or the code
in binomialHeap.h.
For acceleratedBinomialHeap definitions use
binomialHeapA.h.
- (1 point)
A sequence, s = s1, s2, ..., sn,
is a basic binomial Heap sequence if each si is a call to one
of the 4 basic binomial heap functions
Binomial_Heap _Insert(), _Union(), _Minimum(), and _Extract_Min().
Let Tstd(s) be the total time required for the calls in s
if using the standard binomial heap implementation.
Let Tacc(s) be the total time required for the calls in s
using the accelerated binomial heap implementation.
Let T(n) = max({Tstd(s)/Tacc(s) | s is a valid basic binomial heap sequence of length n}).
Explain why T(n) is Ω(lg(n)).