QuickSort—Exploiting the Principle of Exchanging Keys

' QuickSort.  QuickSort, CombSort and ShellSort all exploit the principle of ' exchanging keys that are far apart in the list rather than adjacent.  ' QuickSort does this most elegantly and rapidly.  The approach is to choose a ' "pivot" value (ideally, the median key) and then to work from each end of the ' list toward the middle.  A key at each end is compared to the pivot and ' nothing is done if the left key is less than the pivot or the right key is ' greater.  When a left key greater than the pivot and a right key less than ' the pivot have been found, those keys (or their pointers) are swapped,'  and the process continues until the left and right pointers cross.  We then ' recursively call QuickSort on the left and right sublists until the lists are ' small (and delegate final sorting to low overhead InsertionSort).'' QuickSort does not need any auxiliary arrays, but uses a modest amount of ' stack space for recursion.  It is not stable (although its descendent Ternary ' QuickSort is).  On average, it is the fastest of the O(N log N) sorts,'  but it suffers from rare "worst case" behavior where certain input orders of ' keys cause speed to deteriorate to O(N^2).  Naive implementations of ' QuickSort that choose the middle key for pivot exhibit O(N^2) behavior on ' sorted lists.  The version of QuickSort presented here makes worst case ' behavior very unlikely by choosing the median of the first,'  last and middle keys as pivot.  Two versions are provided.  pQuickSortS is ' set up for strings and can be adapted to doubles by changing the declaration ' of array A().  QuickSortL is set up for longs, or A() can be redeclared for ' integers.  '' Reference:  Robert Sedgewick, "Implementing Quicksort Programs",'  Comm. of the ACM 21(10):847-857 (1978).'' Speed:  pQuickSortS sorts 500,000 random strings in 30.3 sec; sorts 100186 ' library call numbers in 11.3 sec; sorts 25479 dictionary words in 2.0 sec ' (random order), 1.3 sec (presorted) or 1.8 sec (reverse sorted).  QuickSortL ' sorts 500,000 random longs in 56 seconds.  Timed in Excel 2001 on an 800 mhz ' PowerBook.'' Bottom line:  contends with RadixSort for fastest; better adapted than Radix ' for non-string data, but not stable.' Usage:  Dim S1(L To R) As StringDim P1(L To R) As LongDim L1(L To R) As Long For I = L To R    S1(I) = GetRandomString()    P1(I) = I    L1(I) = GetRandomLong()Next IpQuickSortS L, R, S1, P1QuickSortL L, R, L1' CODE:Sub pQuickSortS(L As Long, R As Long, A() As String, P() As Long)    'We put "sentinel" values flanking the real keys to avoid an extra test in     ' the inner loop.    A(L - 1) = MinStr    A(R + 1) = MaxStr    'We mostly sort the list with QuickSort.    pQuickS L, R, A(), P    'Then we finish up with low overhead InsertionSort    pInsertS L, R, A(), PEnd SubSub pQuickS(L As Long, R As Long, A() As String, P() As Long)    Dim MED As Long    Dim LP As Long    Dim RP As Long    Dim Pivot As String    Dim TMP As Long        'Sublists <= 12 keys will be finished by running the whole list once thru     ' InsertionSort.    If R - L > 12 Then    'Get the median pointer...        MED = (L + R)  2    'and swap it to the leftmost position.        TMP = P(MED)        P(MED) = P(L)        P(L) = TMP    'Now compare the leftmost, next leftmost & rightmost to choose a median of     ' 3...        If A(P(L + 1)) > A(P(R)) Then            TMP = P(L + 1)            P(L + 1) = P(R)            P(R) = TMP        End If        If A(P(L)) > A(P(R)) Then            TMP = P(L)            P(L) = P(R)            P(R) = TMP        End If        If A(P(L + 1)) > A(P(L)) Then            TMP = P(L + 1)            P(L + 1) = P(L)            P(L) = TMP        End If    'and use its key as our pivot.        Pivot = A(P(L))    'Now work inward from each end.        LP = L        RP = R + 1        Do        'Scan right for a pointer whose key >= Pivot.  In case Pivot is the         ' largest key, we have        'a sentinel value of MaxStr in A(R + 1) that will end a runaway loop.          ' Using the sentinel        'avoids having a second test in the inner loop,        '  so it can be as fast as possible.            Do                LP = LP + 1            Loop While A(P(LP)) < Pivot        'Scan left for a pointer whose key <= Pivot.  Again,        '  we have a sentinel value of MinStr        'in A(L - 1) to stop the loop if Pivot is the smallest value in the         ' list.             Do                RP = RP - 1            Loop While A(P(RP)) > Pivot        'If the pointers have crossed we're done.            If RP <= LP Then Exit Do        'Otherwise, swap the pair we've identified.            TMP = P(LP)            P(LP) = P(RP)            P(RP) = TMP        Loop    'Swap the pointer of the Pivot value back into place.        TMP = P(L)        P(L) = P(RP)        P(RP) = TMP    'Sort the shorter sublist first so the recursion stack is limited to     ' logarithmic depth.        If (RP - 1) - L <= R - LP Then            pQuickS L, RP - 1, A, P            pQuickS LP, R, A, P        Else            pQuickS LP, R, A, P            pQuickS L, RP - 1, A, P        End If    End IfEnd SubSub pInsertS(L As Long, R As Long, A() As String, P() As Long)    Dim LP As Long    Dim RP As Long    Dim TMP As Long    Dim T As String        For RP = L + 1 To R        TMP = P(RP)        T = A(TMP)        For LP = RP To L + 1 Step -1            If T < A(P(LP - 1)) Then P(LP) = P(LP - 1) Else Exit For        Next LP        P(LP) = TMP    Next RPEnd SubSub QuickSortL(L As Long, R As Long, A() As Long)    A(L - 1) = MinStr    A(R + 1) = MaxStr    QuickL L, R, A    InsertL L, R, AEnd SubSub QuickL(L As Long, R As Long, A() As Long)    Dim MED As Long    Dim LP As Long    Dim RP As Long    Dim Pivot As String    Dim TMP As Long        If R - L > 12 Then        MED = (L + R)  2        TMP = A(MED)        A(MED) = A(L)        A(L) = TMP        If A(L + 1) > A(R) Then            TMP = A(L + 1)            A(L + 1) = A(R)            A(R) = TMP        End If        If A(L) > A(R) Then            TMP = A(L)            A(L) = A(R)            A(R) = TMP        End If        If A(L + 1) > A(L) Then            TMP = A(L + 1)            A(L + 1) = A(L)            A(L) = TMP        End If        Pivot = A(L)        LP = L        RP = R + 1        Do            Do                LP = LP + 1            Loop While A(LP) < Pivot            Do                RP = RP - 1            Loop While A(RP) > Pivot            If RP <= LP Then Exit Do            TMP = A(LP)            A(LP) = A(RP)            A(RP) = TMP        Loop        TMP = A(L)        A(L) = A(RP)        A(RP) = TMP        If (RP - 1) - L < R - LP Then            QuickL L, RP - 1, A            QuickL LP, R, A        Else            QuickL LP, R, A            QuickL L, RP - 1, A        End If    End IfEnd SubSub InsertL(L As Long, R As Long, A() As Long)    Dim LP As Long    Dim RP As Long    Dim TMP As Long        For RP = L + 1 To R        TMP = A(RP)        For LP = RP To L + 1 Step -1            If TMP < A(LP - 1) Then A(LP) = A(LP - 1) Else Exit For        Next LP        A(LP) = TMP    Next RPEnd Sub

Share the Post:
Share on facebook
Share on twitter
Share on linkedin

Overview

The Latest

technology leadership

Why the World Needs More Technology Leadership

As a fact, technology has touched every single aspect of our lives. And there are some technology giants in today’s world which have been frequently opined to have a strong influence on recent overall technological influence. Moreover, those tech giants have popular technology leaders leading the companies toward achieving greatness.

iOS app development

The Future of iOS App Development: Trends to Watch

When it launched in 2008, the Apple App Store only had 500 apps available. By the first quarter of 2022, the store had about 2.18 million iOS-exclusive apps. Average monthly app releases for the platform reached 34,000 in the first half of 2022, indicating rapid growth in iOS app development.

microsoft careers

Top Careers at Microsoft

Microsoft has gained its position as one of the top companies in the world, and Microsoft careers are flourishing. This multinational company is efficiently developing popular software and computers with other consumer electronics. It is a dream come true for so many people to acquire a high paid, high-prestige job