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Fall 2011
CMSC 351: Homework 4
Clyde Kruskal
Due at the start of class Wednesday, October 5, 2011.
Problem 1.
Consider an array of size eight with the numbers in the following order
40
,
20
,
80
,
60
,
30
,
10
,
70
,
50.
(a) Form the heap using the standard (Williams) algorithm. Show the heap as a tree.
Show the heap as an array. Exactly how many comparisons did heap creation
use?
(b) Start with the heap created in Part (a). Show the
array
after each element sifts
down
after heap creation
. How many comparisons does each sift use? What is
the total number of comparisons
after heap creation
?
Problem 2.
We are going to repeat Problem (1) using Floyd’s version for sifting. Consider
an array of size eight with the numbers in the following order 40
,
20
,
80
,
60
,
30
,
10
,
70
,
50.
(a) Form the heap using the Floyd’s sifting algorithm. Show the heap as an array.
Exactly how many comparisons did heap creation use?
(b) Start with the heap created in Part (a). Show the
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 Fall '11
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