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CSE 5311 Design and Analysis of Algorithms
FALL 2007
Department of Computer Science
The University of Texas at Arlington
Exercise Set 2
1)
Answer questions 1a to 1c pertaining to the STOOGE_SORT Algorithm given below.
STOOGE_SORT(A,
i
,
j
)
1
if
A
[
i
] >
A
[
j
]
2
then
exchange
A
[
i
]
↔
A
[
j
]
3
if
i
+1
≥
j
4
then
return
5
k
←
(j-i+1)/3
6
STOOGE_SORT(A,
i
,
j-k
)
7
STOOGE_SORT(A,
i+k
,
j
)
8
STOOGE_SORT(A,
i
,
j-k
)
a.
Argue that STOOGE_SORT (
A
,1,length[
A
]) correctly sorts the input array
A
[1 .
.
n
], where
n
= length[
A
].
b.
Give a recurrence for the worst-case running time of STOOGE_SORT and a tight
asymptotic bound on the worst-case running time.
c.
Compare the worst-case running time of STOOGE_SORT with that of insertion sort,
merge sort, heapsort, and quicksort.
2)
Given an array of integers
A
[1.
.
n
], such that, for all
i
, 1
≤
i
<
n
, we have
A
[
i
]-
A
[
i
+1]
≤
1. Let
A
[1] =
x
and
A
[
n
] =
y
, such that
x
<
y
. Design an efficient search
algorithm to find j such that

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