2/5/08 CS 5633 Analysis of Algorithms 1
CS 5633 -- Spring 2008
Quicksort
Carola Wenk
Slides courtesy of Charles Leiserson with small
changes by Carola Wenk
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Quicksort Algorithm Analysis - Prof. Carola Wenk, Study notes of Algorithms and Programming
An analysis of the quicksort algorithm, including its history, divide and conquer approach, worst-case and best-case running times, and average runtime. It also discusses the concept of randomized quicksort and its advantages.
Typology: Study notes
Pre 2010
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2/5/
CS 5633 Analysis of Algorithms
CS 5633 -- Spring 2008
Quicksort
Carola Wenk
Slides courtesy of Charles Leiserson with small
changes by Carola Wenk
2/5/
CS 5633 Analysis of Algorithms
Quicksort
- Proposed by C.A.R. Hoare in 1962.• Divide-and-conquer algorithm.• Sorts “in place” (like insertion sort, but not
like merge sort).
- Very practical (with tuning).
2/5/
CS 5633 Analysis of Algorithms
Running time=
O
n
) for
n
elements. Running time=
O
n
) for
n
elements.
Partitioning subroutine
P
ARTITION
(
A
,
p
,
q
)
⊳
A
[
p
..
q
]
x
←
A
[
p
]
⊳
pivot =
A
[
p
]
i
←
p
for
j
←
p
- 1
to
q
do if
A
[
j
]
≤
x
then
i
←
i
- 1
exchange
A
[
i
]
↔
A
[
j
]
exchange
A
[
p
]
↔
A
[
i
]
return
i
x x
x
x
x
x
p
i
q
j
Invariant:
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
j
CS 5633 Analysis of Algorithms
Example of partitioning
i
CS 5633 Analysis of Algorithms
Pseudocode for quicksort
Q
UICKSORT
A
p, r
if
p
r
then
q
P
ARTITION
A
p, r
Q
UICKSORT
A
p, q
Q
UICKSORT
A
q+
, r
Initial call:
Q
UICKSORT
A
, n
2/5/
CS 5633 Analysis of Algorithms
Worst-case ofquicksort
- Input sorted or reverse sorted.• Partition around min or max element.• One side of partition always has no elements.
2
n
n
n
T
n
n
T
n n T T n T
(arithmetic series)
CS 5633 Analysis of Algorithms
Worst-case recursion tree
T
n
T
T
n
cn