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COP3530.01, Spring 2001
March 6, 2001
S. Lang
Solution
Key to
Quiz #1
Suppose a binary min-heap consisting of integer values is implemented using array
T
[0.
.
n
] in which
location
T
[0] is left unused and locations
T
[1] through
T
[
n
] store the
n
integer values in the heap,
n
≥
1.
Now answer each of the following questions:
1.
(10 pts.)
(a)
How many leaf nodes does the heap have?
Write your
answer
(as a formula) in terms of
n
, and
give a brief
explanation
.
(A node is a leaf node if it has zero child nodes.)
The last node’s index is
n
, so its parent’s index is
n
/2
and this is the non-leaf node with the
highest index.
Thus, there are
n
/2
non-leaf nodes, so the number of leaf nodes is
n
–
n
/2
=
n
/
2
.
(b) Give the time complexity in terms of
n
for each of the following operations (no explanation
needed):
findMin() – O(1).
deleteMin( ) – O(lg
n
).
findHeight( ) – O(lg

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