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Quick Sort. Quick Sort. Divide : Pick any element p as the pivot , e.g, the first element Partition the remaining elements into FirstPart, which contains all elements < p SecondPart, which contains all elements ≥ p Recursively sort the FirstPart and SecondPart

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Quick Sort

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Quick Sort


Quick Sort

  • Divide:

    • Pick any element p as the pivot, e.g, the first element

    • Partition the remaining elements into

      FirstPart,which contains all elements< p

      SecondPart, which contains all elements ≥ p

  • Recursively sort the FirstPart and SecondPart

  • Combine: no work is necessary since sorting

    is done in place


  • Partition

    Recursive call

    p

    p

    p

    p ≤ x

    p ≤ x

    Sorted

    FirstPart

    Sorted

    SecondPart

    x < p

    Quick Sort

    A:

    pivot

    FirstPart

    SecondPart

    x < p

    Sorted


    Quick Sort

    Quick-Sort(A, left, right)

    ifleft ≥ right return

    else

    middle ← Partition(A, left, right)

    Quick-Sort(A, left, middle–1 )

    Quick-Sort(A, middle+1, right)

    end if


    p

    x < p

    p

    p ≤ x

    x < p

    p ≤ x

    p

    Partition

    A:

    A:

    A:

    p


    Partition Example

    A:

    4

    8

    6

    3

    5

    1

    7

    2


    Partition Example

    i=0

    A:

    4

    8

    6

    3

    5

    1

    7

    2

    j=1


    Partition Example

    i=0

    A:

    4

    8

    6

    3

    5

    1

    7

    2

    8

    j=1


    Partition Example

    i=0

    A:

    4

    8

    6

    6

    3

    5

    1

    7

    2

    j=2


    i=1

    3

    8

    Partition Example

    i=0

    A:

    4

    6

    3

    5

    1

    7

    2

    8

    3

    j=3


    i=1

    Partition Example

    A:

    4

    3

    6

    8

    5

    1

    7

    2

    5

    j=4


    i=1

    Partition Example

    A:

    4

    3

    6

    8

    5

    1

    1

    7

    2

    j=5


    i=2

    1

    6

    Partition Example

    A:

    4

    3

    6

    8

    5

    1

    7

    2

    j=5


    i=2

    Partition Example

    A:

    7

    4

    3

    1

    8

    5

    6

    7

    2

    j=6


    i=2

    i=3

    Partition Example

    A:

    8

    2

    2

    4

    3

    1

    8

    5

    6

    7

    2

    j=7


    i=3

    Partition Example

    A:

    4

    3

    1

    2

    5

    6

    7

    8

    j=8


    i=3

    Partition Example

    A:

    4

    4

    3

    1

    2

    5

    6

    7

    8

    2


    x < 4

    4 ≤ x

    Partition Example

    pivot in

    correct position

    A:

    2

    4

    3

    1

    5

    6

    7

    8


    Partition(A, left, right)

    • x ← A[left]

    • i ← left

    • for j ← left+1 to right

    • if A[j] < x then

    • i ← i + 1

    • swap(A[i], A[j])

    • end if

    • end for j

    • swap(A[i], A[left])

    • return i

    n = right – left +1

    Time: cn for some constant c

    Space: constant


    2 3 1

    4

    5 6 7 8

    Quick-Sort(A, 0, 7)

    Partition

    A:

    4 8 6 3 5 1 7 2


    1

    3

    2

    Quick-Sort(A, 0, 7)

    , partition

    Quick-Sort(A, 0, 2)

    A:

    5 6 7 8

    4

    2 3 1


    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 0, 0)

    , base case

    , return

    5 6 7 8

    4

    3

    1

    2

    1


    3

    3

    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 1, 1)

    , base case

    5 6 7 8

    4

    1

    2


    1

    1

    3

    3

    2

    2

    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 0, 2), return

    Quick-Sort(A, 2, 2),return

    5 6 7 8

    4


    5 6 7 8

    6 7 8

    5

    1

    3

    2

    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 4, 7)

    , partition

    Quick-Sort(A, 2, 2),return

    4


    1

    3

    2

    6

    7 8

    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 5, 7)

    , partition

    4

    5

    6

    6 7 8


    1

    3

    2

    Quick-Sort(A, 0, 7)

    Quick-Sort(A, 6, 7)

    , partition

    4

    5

    6

    7

    7 8

    8


    1

    3

    2

    Quick-Sort(A, 0, 7)

    , return

    , base case

    Quick-Sort(A, 7, 7)

    4

    5

    6

    7

    8

    8


    1

    3

    2

    Quick-Sort(A, 0, 7)

    , return

    Quick-Sort(A, 6, 7)

    4

    5

    6

    7

    8


    1

    3

    2

    6

    7

    8

    Quick-Sort(A, 0, 7)

    , return

    Quick-Sort(A, 5, 7)

    4

    5


    5

    1

    3

    2

    6

    7

    8

    Quick-Sort(A, 0, 7)

    , return

    Quick-Sort(A, 4, 7)

    4


    5

    1

    3

    2

    6

    7

    8

    Quick-Sort(A, 0, 7)

    , done!

    Quick-Sort(A, 0, 7)

    4


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