Quicksort Algorithm

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Quicksort Algorithm
Department of Computer and Information
Science,School of Science, IUPUI
Dale Roberts, Lecturer Computer Science,
IUPUI E-mail droberts_at_cs.iupui.edu
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Notes on Quicksort

• Quicksort was invented in 1960 by C. A. R. Hoare.
• Quicksort is more widely used than any other
  sort.
• Quicksort is well-studied, not difficult to
  implement, works well on a variety of data, and
  consumes fewer resources that other sorts in
  nearly all situations.
• Quicksort is O(nlog n) time, and O(log n)
  additional space due to recursion.

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Notes on Quicksort

• Quicksort has withstood the test of time. It has
  been thoroughly analyzed. The analysis has been
  verified through extensive empirical experience.
• Quicksort is not stable.
• Quicksort performance can degenerate under
  special circumstances. It is possible modify the
  algorithm to handle these cases, but at the
  expense of making the algorithm more complicated.
• Sedgewick states that tuning Quicksort is the
  better mousetrap of computer science. Many
  ideas have been tried, but its easy to be
  deceived because the algorithm is so balanced
  that a perceived improvement in one area can be
  more than offset by poor performance in another
  area.

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Quicksort Algorithm

• Quicksort is a divide-and-conquer method for
  sorting. It works by partitioning an array into
  parts, then sorting each part independently.
• The crux of the problem is how to partition the
  array such that the following conditions are
  true
• There is some element, ai, where ai is in its
  final position.
• For all l lt i, al lt ai.
• For all i lt r, ai lt ar.

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Quicksort Algorithm (cont)

• As is typical with a recursive program, once you
  figure out how to divide your problem into
  smaller subproblems, the implementation is
  amazingly simple.
• int partition(Item a, int l, int r)
• void quicksort(Item a, int l, int r)
• int i
• if (r lt l) return
• i partition(a, l, r)
• quicksort(a, l, i-1)
• quicksort(a, i1, r)

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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

Q
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

Q
U
I
C
K
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O
R
T
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

Q
U
I
C
K
S
O
R
T
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S
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O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
U
I
C
K
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L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
U
I
C
K
S
O
R
T
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
U
I
C
K
S
O
R
T
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O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
U
I
C
K
S
O
R
T
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O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

C
I
I
C
K
S
O
R
T
U
S
Q
O
O
L
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

swap with partitioning element
pointers cross
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Partitioning in Quicksort

• How do we partition the array efficiently?
• choose partition element to be rightmost element
• scan from left for larger element
• scan from right for smaller element
• exchange
• repeat until pointers cross

partition is complete
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Partitioning in Quicksort

• int partition(Item a, int l, int r)
• int i l-1, j r Item v ar
• for ()
• while (less(ai, v))
• while (less(v, a--j)) if (j l)
  break
• if (i gt j) break
• exch(ai, aj)
• exch(ai, ar)
• return i

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Quicksort Demo

• Quicksort illustrates the operation of the basic
  algorithm. When the array is partitioned, one
  element is in place on the diagonal, the left
  subarray has its upper corner at that element,
  and the right subarray has its lower corner at
  that element. The original file is divided into
  two smaller parts that are sorted independently.
  The left subarray is always sorted first, so the
  sorted result emerges as a line of black dots
  moving right and up the diagonal.