指针和数组混淆的 K&R Qsort 示例

Question

我发现很难理解下面的代码片段。 我理解所显示的指向函数风格的指针，但我发现混乱之处在于指示的行中。

void qsort(void **v, int left, int right, int (*comp) (void *, void *))
{
    int i, last;
    void swap(int **v, int i, int j);

    if (left >= right)   /* do nothing if array contains */
        return;           /* fewer than two elements */
    swap(v, left, (left + right)/2);   /* move partition elem */ [1]
    last = left;                       /* to v[0] */ [2]
    for (i = left + 1; i <= right; i++) /* partition */ [3]
        if ((*comp) (v[i], v[left]) < 0) [4]
            swap(v, ++last, i); [5]
    swap(v, left, last);        /* restore partition elem */ [6]
    qsort(v, left, last - 1); [7]
    qsort(v, last + 1, right);  [8]

}

有人可以向我解释这个例程，特别是指示的行，只需告诉我它在做什么，因为我无法弄清楚这个 qsort，我在阅读 k&r 时阅读的爱斯基摩指南说 qsort 例程是垃圾，而且过度复杂的。 我只需要理解为什么这样写，因为这对我来说毫无意义。

感谢您阅读本文，即使没有任何意义。

Answer 1

这是一段漂亮的代码！

首先，了解快速排序背后的想法很重要：

1）获取数字列表。

2) 选择一个，称之为 X。

3) 制作两个列表，其中一个是所有小于 X 的数字，一个是所有大于 X 的数字。

4) 对小于 X 的数字进行排序。对大于 X 的数字进行排序。

这个想法是，如果我们幸运地为 X 选择一个好的值，那么小于 X 的数字列表的大小与大于 X 的数字列表的大小相同如果我们从 2*N+1 个数字开始，那么我们会得到两个包含 N 个数字的列表。 每次，我们希望除以二，但我们必须对 N 个数字进行排序。 我们可以将 N 除以 2 多少次？ 这就是 Log(N)。
所以，我们排序 N Log(N) 次。 这很棒！

至于代码是如何工作的，这里是运行过程，还有一些草图。 我们将选择一个小数组:)

这是我们的数组：[DACBE]

在开始，左= 0，指向D。右= 4，指向E。

现在，按照代码，带有您的标签：

[1]交换(v,0,2)[DACBE]→ [CADBE]

我们已经交换了选择的值并将其放在数组的开头。

[2] last=0

这有点聪明......我们想保留一个计数器，这样我们就知道哪些值更大，哪些值更小......你会看到它是如何进展的

[3] for (i=1;i< ;=4;i++)

对于列表中的所有剩余元素...

[4] if ((*comp)(v[i], 'C')<0)

如果 i 处的值小于 'C '...

[5] 交换(v,++last,i);

把它放在列表的开头！

代码

让我们运行 3,4,5 i=1 的

： [CADBE]

if ('A'<'C')

swap('A','A') (AND INCRMENT LAST!)

[CADBE]->; [CADBE]（无变化）

last=1

i=2：

[CADBE]

if ('D'<'C')

失败。 继续前行。

i=3:

[CADBE]

if ('B'<'C')

swap('B','D') 最后递增！

[CADBE]-> [CABDE]（看它！正在排序！）

last=2

i=4:

[CABDE]

if ('E'<'C')

失败。 继续前行。

好吧，艾斯。 这样循环给出的是 [CABDE], last=2 ('B')

现在第 [6] 行.... swap(left,last)... 那是 swap('C','B')
[CABDE]-> [BACDE]

现在，它的神奇之处在于......它是部分排序的！ BA < C＜ 德！

现在我们对子列表进行排序！

[7]-> [BA]-> [AB]

所以

[BACDE]-> [ABCDE]

[8]-> [DE]->[DE]

所以

[ABCDE]-> [ABCDE]

我们就完成了！

Answer 2

K&R 的快速排序是优秀编码的一个例子，但不是快速排序工作原理的一个很好的例子。 预交换的目的并不直观，身份交换效率低下且令人困惑。 我编写了一个程序来帮助澄清这一点。 代码注释解释了问题。

我仅在 Linux 下进行编译和测试，但 Visual Studio 对于这个普通的控制台应用程序应该没有问题。

/***************************** QUICK.CPP ***************************************
Author: David McCracken
Updated: 2009-08-14

Purpose: This illustrates the operation of the quicksort in K&R "The C 
Programming Language" (second edition p. 120). Many programmers are frustrated 
when they attempt to understand quicksort in general from this version, which 
was clearly not intended as a tutorial on quicksort but on the use of pointers 
to functions. My program modifies the original to work only on ints in order to 
focus on the sorting process. It can print the global list and recursive 
sublist at each change to trace the sorting decision process. My program also 
clarifies two confusing aspects, both involving unexplained swapping, of the 
original by comparing its operation to that of two further modified versions.

One confusing thing that the original does is to swap an item with itself.
The code (modified for ints only)  is:

last = left;
for( i = left+1 ; i <= right ; i++ )
   if(  v[i] < v[ left ] )
       swap( v[ ++last ], v[ i ]);
Note that left and v[ left ] are loop-invariant. v[ left ] is the pivot. 

A superfluous swap is performed on all values less than the pivot without an 
earlier value greater than the pivot. For example, given  sublist (after 
preswap) 9,8,5,7,4,6, initially i = left + 1, selecting 8. Since this is less 
than 9, last is incremented to point to the same element as i (selecting 8) and 
a superfluous swap is performed. At the next iteration, last selects 8 while i 
selects 5 and 5 is swapped with itself. This continues to the end of the 
sublist. The sorting function krQuick2 is identical to krQuick but tests ++last 
against i to avoid superfluous swapping. This certainly yields better 
performance for practically no cost but, more importantly, helps to clarify 
just what the code is trying to do, which is to find and swap a value that is 
larger than the pivot with one that occurs later and is smaller than the pivot. 

A second source of confusion is the purpose of the preswap, where the midpoint 
value is swapped with the left-most. Since this is done without regard to 
value, it cannot decrease entropy. In fact, it does exactly the opposite in the 
very important case of a sublist that is already sorted, which normally makes 
quicksort perform badly. This action deliberately unsorts a sorted list and 
essentially does nothing to an unsorted one. This simple and cheap action 
substantially improves average and worst case performance, as demonstrated by 
the third variation, quick3, which just removes the preswap from krQuick2. 
quick3 demonstrates that the preswap is not required; in fact that any value 
can be chosen from the list to serve as the pivot. Only in the most unsorted 
cases does quick3 exhibit slightly better performance than krQuick2 by virture 
of skipping the preswap. With increasing initial order, the performance of 
krQuick2 steadily improves over quick3.

Some confusion may also come from the testing of v[i] against v[left]. left and 
v[ left ] are loop-invariant. An optimizing compiler should recognize this and 
hoist the value out of the loop, but this loop-invariance is not immediately 
obvious to someone studying this as an example of quicksort. During the swap 
loop, v[left] serves only to hold the pivot value. An automatic could just as 
easily hold the value and its purpose would be more clear. However, the code is 
an example of indirection. We don't know what the list items are but we can be 
sure that any one of them can fit into v[ left ] and that the swap function can 
put it there. Thus, the one preswap operation does three things; it randomizes 
a sorted sublist; it conveniently copies the pivot to a place where it won't be 
subject to swapping; and it fills the hole in the loop left by extracting the 
pivot. It does all of this without even knowing what the elements are and with 
a function that we already have. This amazing programming feat is well worth 
studying but not in the interest of understanding quicksort.

                         HOW TO USE THIS PROGRAM
There are three general variables, the function, the data to be sorted, and what
to display. 

The simplified K&R original function, krQuick, is function 0. Function 1, 
krQuick2, is krQuick with identity swaps removed. Function 2, quick3, is 
krQuick2 without preswap.

The data to be sorted can be any one of five builtin lists or all of them or
a space-delimited list of decimal ints entered on the command line.

The displayed information affords a trace of the function's operation. In all 
cases, the list is displayed before and after sorting, and executing statistics
are reported. If SHOW_NOTHING then nothing else is reported. If SHOW_GLOBAL, 
the changing full list is displayed at each invocation of the recursive sort 
function. If SHOW_LOCAL1, the sublist passed to the function is displayed before
it is modified. If SHOW_LOCAL, the sublist is displayed after each swap. If 
SHOW_INDEX, the indices involved in swapping and the values at those indices 
are shown before the swap occurs.These selections correspond to the SHOW_ enum 
and are culmulative flags.

By default, all three functions are applied in succession to all five builtin 
data lists, with SHOW_NOTHING. This is useful for comparing the performance of 
the functions. For example, it shows that on the unordered list 11 0 10 1 9 2 8 
3 7 4 6 5 quick3 uses 37 compares and 30 swaps while krQuick2 uses 38 compares 
and 44 swaps. However, on the ordered list 0 1 2 3 4 5 6 7 8 9 10 11 quick3
uses 66 compares and 22 swaps while krQuick2 uses 25 compares and 28 swaps.

Command line arguments alter the content but not the order of operation. In all
cases, each selected function is applied to all selected data lists.
Command arguments are case-insensitive: F function selector, D data selector,
and S show what map. Each is followed without space by a single character.
F0, F1, F2, FA select function 0, 1, or 2 only or all functions.
D0, D1, D2, D3, D4, DA select builtin data list 0, 1, 2, 3, or 4 only or all.
S0 (default) shows no extra information.
S1 (GLOBAL) shows the full list (without "GLOBAL" legend) at each invocation.
S2 (LOCAL1) shows the sublist before processing. 
S3 (GLOBAL+LOCAL1) 
S4 (LOCAL) shows the sublist after each swap. It also shows the sublist before
    processing.
S8 (INDEX) shows indices but these would never be shown without at least LOCAL,
    which can't be combined with 8 in the single-digit argument.
SA (All) 
Note that the Local legend includes a numeric suffix to identify where in the
point in the code that is reporting.
The most useful S formats are S1, S5, and SA (S0 is default).

After any F and S arguments, any space-delimited list of numbers will be taken
as the data list. Any D argument is ignored. For example:
quick 20 21 15 12 40 0
applies all three functions to the data, reporting only the unsorted and sorted
full lists and operational statistics.
quick f0 sa 20 21 15 12 40 0
applies only function 0 krQuick to the data, reporting everything. 

*******************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

// ======================== DATA AND DECLARATIONS ===============================
#define DIM(A) ( sizeof A / sizeof A[0])
typedef unsigned int UINT;

enum { SHOW_NOTHING, SHOW_GLOBAL = 1, SHOW_LOCAL1 = 2, SHOW_LOCAL = 4, 
       SHOW_INDEX = 8, SHOW_ALL = 0xFF };

int showWhat = SHOW_NOTHING;

int list0[] = { 4,0,2,5,1,3 };
int list1[] = { 0,1,2,3,4,5,6,7,8,9,10,11 };
int list2[] = { 11,10,9,8,7,6,5,4,3,2,1,0 };
int list3[] = { 11,9,7,5,3,1,0,2,4,6,8,10 };
int list4[] = { 11,0,10,1,9,2,8,3,7,4,6,5 };
static struct { int *list; int cnt; } lists[] = 
{ 
    { list0, DIM( list0 )},
    { list1, DIM( list1 )},
    { list2, DIM( list2 )},
    { list3, DIM( list3 )},
    { list4, DIM( list4 )},
};

int total[ 1000 ];
int totalCnt;
int *userData = 0;
int userDataLen = 0;

int recursion;  // Current recursion level.
int calls;      // Number of times the sort function is called.
int depth;      // Maximum recursion level.
int swaps;      // Count of swaps.
int compares;   // Count of list item compares.
int totCalls;
int totDepth;
int totCompares;
int totSwaps;

void (*sortFunc)( int *list, int left, int right );

char dArg = 'A'; // command line argument selects 0,1,2,3,4, or A
int dataList; // If dArg is numeric, this is its int value.

//============================== FUNCTIONS =====================================

// ------------------------------ indent --------------------------------------
// Print two spaces for each level of recursion to indent subsequent print 
// output.
// ............................................................................
void indent( void )
{
    for( int indent = 1 ; indent < recursion ; indent++ )
        printf( "  " );
}

// -------------------------------- show ---------------------------------------
// Print the given int list according to the global control setting showWhat 
// and the given local identification. This may print nothing or the global 
// list or the local sublist. It may or may not print the legend GLOBAL or 
// LOCALx where x is the local ID, which tells at what point in the sort code 
// we are showing the sublist.
// Returns: Nothing
// Arguments:
//- int *ia points to the int list.
//- int cnt is the number of elements in the list.
//- int local tells the local point in the sort routine if greater than 0. 0 
// indicates that this is global. In either case, format is controlled by
// showWhat. If local is -1, the list is printed unconditionally and without
// any legend.
// Global:
//- showWhat bitmapped control word
//-- 0 (SHOW_NOTHING) This is the complete value, not a bit flag.
//-- 1 (SHOW_GLOBAL) Print the list if local is 0. If any other bit is also
// set, the GLOBAL legend is printed before the list.
//-- 2 (SHOW_LOCAL1) Print the list only if local is 1.
//-- 3 (SHOW_LOCAL) Print the list if local is 1 or greater.
//
// ...................... notes .............................................
//                     SHOW_NOTHING
// This exists because the callers don't test showWhat before calling. If we 
// only want to show the initial unsorted list and final sorted version then 
// SHOW_NOTHING blocks all print output from the sort function. The control 
// function calls show with local = -1 to print the list.
// ..........................................................................
void show( int *ia, int cnt, int local )
{
    if( local >= 0 )
    {
        switch( showWhat )
        {
        case SHOW_NOTHING:
            return;
        case SHOW_GLOBAL:   // Only SHOW_GLOBAL
            if( local > 0 )
                return;     // This is a local
            break;          // Print list without legend.
        default: // Some combination of SHOW_GLOBAL, SHOW_LOCAL1, SHOW_LOCAL
            if( local == 0 ) // global
            {
                if( ( showWhat & SHOW_GLOBAL ) == 0 )
                    return;
                printf( "GLOBAL " );
            }
            else if( showWhat & SHOW_LOCAL || ( showWhat & SHOW_LOCAL1 && local == 1 ))
            {
                indent();
                printf( "Local%d: ", local );
            }
            else
                return;
        }
    }
    for( int *end = ia + cnt ; ia < end ; ia++ )
        printf( "%d ", *ia );
    putchar( '\n' );
}

// -------------------------------- swap ---------------------------------------
void swap( int *p1, int *p2 )
{
    int temp = *p2;
    *p2 = *p1;
    *p1 = temp;
    ++swaps;
}

// ------------------------------ krQuick --------------------------------------
// K&R's quick function modified to handle only integers and to use inline 
// numeric comparison instead of an indirect comp function.
// .............................................................................
void krQuick( int *list, int left, int right )
{
    int i, last;

    ++calls;
    if( recursion > depth )
        depth = recursion; // At first call recursion = 0 and depth is 0, i.e. no recursion yet.
    ++recursion;
    show( total, totalCnt, 0 ); // GLOBAL
    show( list + left, right - left + 1, 1 ); // LOCAL
    if( left < right )
    {
        swap( list + left, list + (left + right) / 2 );
        ++swaps;
        show( list + left, right - left + 1, 2 );
        last = left;
        for( i = left + 1 ; i <= right ; i++ )
        {
            ++compares;
            if( list[ i ] < list[ left ])
            {
                if( showWhat & SHOW_INDEX )
                {
                    indent();
                    printf( "i=%d @i=%d left=%d @left=%d last=%d\n", 
                      i, list[i], left, list[ left ], last );
                }
                swap( list + ++last, list + i );
                show( list + left, right - left + 1, 3 );
                ++swaps;
            }
        }
        swap( list + left, list + last );
        show( list + left, right - left + 1, 4 );
        ++swaps;
        krQuick( list, left, last - 1 );
        krQuick( list, last + 1, right );
    }
    --recursion;
}

// ------------------------------- krQuick2 ------------------------------------
// K&R's quick function modified as in krQuick plus elimination of identity 
// swaps.
// .............................................................................
void krQuick2( int *list, int left, int right )
{
    int i, last;

    ++calls;
    if( recursion > depth )
        depth = recursion; // At first call recursion = 0 and depth is 0, i.e. no recursion yet.
    ++recursion;
    show( total, totalCnt, 0 ); // GLOBAL
    show( list + left, right - left + 1, 1 ); // LOCAL
    if( left < right )
    {
        swap( list + left, list + (left + right) / 2 );
        ++swaps;
        show( list + left, right - left + 1, 2 );
        last = left;
        for( i = left + 1 ; i <= right ; i++ )
        {
            ++compares;
            if( list[ i ] < list[ left ] && ++last != i )
            {
                if( showWhat & SHOW_INDEX )
                {
                    indent();
                    printf( "i=%d @i=%d left=%d @left=%d last=%d\n", 
                      i, list[i], left, list[ left ], last );
                }
                swap( list + last, list + i );
                show( list + left, right - left + 1, 3 );
                ++swaps;
            }
        }
        swap( list + left, list + last );
        show( list + left, right - left + 1, 4 );
        ++swaps;
        krQuick2( list, left, last - 1 );
        krQuick2( list, last + 1, right );
    }
    --recursion;
}

// ------------------------------------ quick3 ---------------------------------
// krQuick2 modified to not do the preswap. In the K&R original, the purpose of
// the preswap is to introduce randomness into a presorted sublist. The sorting
// result is not changed by eliminating this but the performance degrades with
// more compares and swaps in all cases between average and worst. Only near the
// best case does eliminating the preswap improve performance.
// ............................................................................
void quick3( int *list, int left, int right )
{
    int i, last;

    ++calls;
    if( recursion > depth )
        depth = recursion; // At first call recursion = 0 and depth is 0, i.e. no recursion yet.
    ++recursion;
    show( total, totalCnt, 0 ); // GLOBAL
    show( list + left, right - left + 1, 1 ); // LOCAL
    if( left < right )
    {
        last = left;
        for( i = left + 1 ; i <= right ; i++ )
        {
            ++compares;
            if( list[ i ] < list[ left ] && ++last != i )
            {
                if( showWhat & SHOW_INDEX )
                {
                    indent();
                    printf( "i=%d @i=%d left=%d @left=%d last=%d\n", 
                      i, list[i], left, list[ left ], last );
                }
                swap( list + last, list + i );
                show( list + left, right - left + 1, 3 );
                ++swaps;
            }
        }
        swap( list + left, list + last );
        show( list + left, right - left + 1, 4 );
        ++swaps;
        quick3( list, left, last - 1 );
        quick3( list, last + 1, right );
    }
    --recursion;
}

static struct { void (*func)( int *list, int left, int right ) ; char *name ; } sortFuncs[] =
{
    { krQuick, (char*)"krQuick" }, 
    { krQuick2, (char*)"krQuick2 (no identity swaps)" },
    { quick3, (char*)"quick3 (no preswaps)" }
};

// ------------------------------------ sortOne --------------------------------
// Set up performance counters, invoke the currently selected sort on the current
// data list, and print the performance (for this one case of selected function
// applied to selected data list).
// .............................................................................
void sortOne( void )
{
    recursion = 0;
    calls = 0;
    depth = 0;
    swaps = 0;
    compares = 0;
    show( total, totalCnt, -1 );
    sortFunc( total, 0, totalCnt - 1 );
    show( total, totalCnt, -1 );
    printf( "Calls = %d, depth = %d, compares = %d, swaps = %d\n", 
      calls, depth, compares, swaps );
    printf( "---------------------------------\n" );
}

// ---------------------------- sortOneSet -------------------------------------
// Purpose: Apply the currently selected sort function to one data list.
void sortOneSet( int idx )
{
    if( idx < 0 )
    {
        totalCnt = userDataLen;
        memcpy( total, userData, totalCnt * sizeof( int ));
    }
    else
    {
        totalCnt = lists[ idx ].cnt;
        memcpy( total, lists[ idx ].list, totalCnt * sizeof( int ));
    }   
    sortOne();
    totCalls += calls;
    totDepth += depth;
    totCompares += compares;
    totSwaps += swaps;
}

// ------------------------- testOneFunc ---------------------------------------
// Purpose: Apply the selected function to one or all data lists.
// Returns: Nothing
// Arguments: int sel is 0,1,or 2, selecting krQuick, krQuick2, or quick3.
// Globals: char dArg is the data list selector command line argument. It is '0',
// '1', '2', or 'A'. 'A' selects all data lists. Otherwise, int dataList is the
// int value of dArg, which has already been translated for us by the command
// line processor.
// .............................................................................
void testOneFunc( int sel )
{
    totCalls = 0;
    totDepth = 0;
    totCompares = 0;
    totSwaps = 0;
    sortFunc = sortFuncs[ sel ].func;
    printf( "====== %s ======\n", sortFuncs[ sel ].name );

    if( userDataLen != 0 )
        sortOneSet( -1 );
    else if( dArg == 'A' )
    {
        for( UINT idx = 0 ; idx < DIM( lists ) ; idx++ )
            sortOneSet( idx );
        printf( "Total: calls = %d, depth = %d, compares = %d, swaps = %d\n",
          totCalls, totDepth, totCompares, totSwaps );
    }
    else 
        sortOneSet( dataList );
}

// --------------------------------- main --------------------------------------
// Purpose: Process command line arguments, set up show (print output) and data 
// list selectors, and invoke testOneFunc either once for the selected function 
// or for each of the three functions.
// .............................................................................
int main( int argc, char **argv )
{
    char    *cp;
    char    fArg = 'A'; // function selector 0,1,2,A
    UINT    idx;

    showWhat = SHOW_NOTHING;
    dArg = 'A';
    for( int cnt = 1 ; cnt < argc ; cnt++ )
    {
        cp = argv[ cnt ];
        switch( toupper( *cp ))
        {
        case 'F':
            fArg = toupper( cp[1] );
            break;
        case 'D':
            dArg = toupper( cp[1] );
            if( dArg != 'A' )
            {
                dataList = dArg - '0';
                if( dataList < 0 || dataList >= (int)DIM( lists ))
                {
                    printf( "Error: bad data list selector %c\n", dArg );
                    return 1;
                }
            }
            break;
        case 'S': // show selector matches bit-mapped showWhat or N or A
            ++cp;
            if( *cp != 0 || toupper( *cp ) != 'N' )
            {
                if( toupper( *cp ) == 'A' )
                    showWhat = SHOW_ALL;
                else
                    showWhat = atoi( cp );
            }
            break;
        default:
            if( !isdigit( *cp ))
            {   
                printf( "Error: There is no option %c\n", *cp );
                return 1;
            }
            for( idx = 0 ; idx < DIM( total ) && cnt < argc ; idx++, cnt++ )
                total[ idx ] = atoi( argv[ cnt ] );
            userData = (int*)malloc( sizeof( int ) * idx );
            if( userData == 0 )
            {
                printf( "Error: Unable to allocate memory for data list\n" );
                return 2;
            }
            memcpy( userData, total, sizeof( int ) * idx );
            userDataLen = idx;
        }
    }
    switch( fArg )
    {
    case 'A':
        for( UINT sfi = 0 ; sfi < DIM( sortFuncs ) ; sfi++ )
            testOneFunc( sfi );
        break;
    case '0':
    case '1':
    case '2':
        testOneFunc( fArg - '0' );
        break;
    default:
        printf( "Error: bad function selector %c\n", fArg );
        return 1;
    }
    return 0;
}

Results of quick
This uses all defaults, which is most useful for comparing the performance
of the three different functions.

====== krQuick ======
4 0 2 5 1 3 
0 1 2 3 4 5 
Calls = 7, depth = 2, compares = 8, swaps = 20
---------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 3, compares = 25, swaps = 48
---------------------------------
11 10 9 8 7 6 5 4 3 2 1 0 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 17, depth = 5, compares = 30, swaps = 62
---------------------------------
11 9 7 5 3 1 0 2 4 6 8 10 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 13, depth = 5, compares = 33, swaps = 56
---------------------------------
11 0 10 1 9 2 8 3 7 4 6 5 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 6, compares = 38, swaps = 60
---------------------------------
Total: calls = 67, depth = 21, compares = 134, swaps = 246
====== krQuick2 (no identity swaps) ======
4 0 2 5 1 3 
0 1 2 3 4 5 
Calls = 7, depth = 2, compares = 8, swaps = 16
---------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 3, compares = 25, swaps = 28
---------------------------------
11 10 9 8 7 6 5 4 3 2 1 0 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 17, depth = 5, compares = 30, swaps = 52
---------------------------------
11 9 7 5 3 1 0 2 4 6 8 10 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 13, depth = 5, compares = 33, swaps = 46
---------------------------------
11 0 10 1 9 2 8 3 7 4 6 5 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 6, compares = 38, swaps = 44
---------------------------------
Total: calls = 67, depth = 21, compares = 134, swaps = 186
====== quick3 (no preswaps) ======
4 0 2 5 1 3 
0 1 2 3 4 5 
Calls = 7, depth = 3, compares = 10, swaps = 10
---------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 23, depth = 11, compares = 66, swaps = 22
---------------------------------
11 10 9 8 7 6 5 4 3 2 1 0 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 23, depth = 11, compares = 66, swaps = 22
---------------------------------
11 9 7 5 3 1 0 2 4 6 8 10 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 7, compares = 46, swaps = 54
---------------------------------
11 0 10 1 9 2 8 3 7 4 6 5 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 19, depth = 6, compares = 37, swaps = 30
---------------------------------
Total: calls = 87, depth = 38, compares = 225, swaps = 138

*******************************************************************************

Results of quick f0 s5 d1
S5 format is best for displaying how the sublist changes during sorting. Since 
LOCAL is displayed only after a swap, superfluous identity swaps (many in this 
example) are readily apparent.

====== krQuick ======
0 1 2 3 4 5 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
Local1: 0 1 2 3 4 5 6 7 8 9 10 11 
Local2: 5 1 2 3 4 0 6 7 8 9 10 11 
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local4: 0 1 2 3 4 5 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
  Local1: 0 1 2 3 4 
  Local2: 2 1 0 3 4 
  Local3: 2 1 0 3 4 
  Local3: 2 1 0 3 4 
  Local4: 0 1 2 3 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 0 1 
    Local2: 0 1 
    Local4: 0 1 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 1 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 3 4 
    Local2: 3 4 
    Local4: 3 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
  Local1: 6 7 8 9 10 11 
  Local2: 8 7 6 9 10 11 
  Local3: 8 7 6 9 10 11 
  Local3: 8 7 6 9 10 11 
  Local4: 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 6 7 
    Local2: 6 7 
    Local4: 6 7 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 7 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 9 10 11 
    Local2: 10 9 11 
    Local3: 10 9 11 
    Local4: 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 9 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 11 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 3, compares = 25, swaps = 48

********************************************************************************

Results of quick f0 sa d1
This is the same as the previous example but shows the additional detail of index
values that lead to the swapping decision. However, the clutter tends to obscure
what is actually happening to the sublist.

====== krQuick ======
0 1 2 3 4 5 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
Local1: 0 1 2 3 4 5 6 7 8 9 10 11 
Local2: 5 1 2 3 4 0 6 7 8 9 10 11 
i=1 @i=1 left=0 @left=5 last=0
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
i=2 @i=2 left=0 @left=5 last=1
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
i=3 @i=3 left=0 @left=5 last=2
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
i=4 @i=4 left=0 @left=5 last=3
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
i=5 @i=0 left=0 @left=5 last=4
Local3: 5 1 2 3 4 0 6 7 8 9 10 11 
Local4: 0 1 2 3 4 5 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
  Local1: 0 1 2 3 4 
  Local2: 2 1 0 3 4 
  i=1 @i=1 left=0 @left=2 last=0
  Local3: 2 1 0 3 4 
  i=2 @i=0 left=0 @left=2 last=1
  Local3: 2 1 0 3 4 
  Local4: 0 1 2 3 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 0 1 
    Local2: 0 1 
    Local4: 0 1 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 1 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 3 4 
    Local2: 3 4 
    Local4: 3 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 4 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
  Local1: 6 7 8 9 10 11 
  Local2: 8 7 6 9 10 11 
  i=7 @i=7 left=6 @left=8 last=6
  Local3: 8 7 6 9 10 11 
  i=8 @i=6 left=6 @left=8 last=7
  Local3: 8 7 6 9 10 11 
  Local4: 6 7 8 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 6 7 
    Local2: 6 7 
    Local4: 6 7 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 7 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
    Local1: 9 10 11 
    Local2: 10 9 11 
    i=10 @i=9 left=9 @left=10 last=9
    Local3: 10 9 11 
    Local4: 9 10 11 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 9 
GLOBAL 0 1 2 3 4 5 6 7 8 9 10 11 
      Local1: 11 
0 1 2 3 4 5 6 7 8 9 10 11 
Calls = 15, depth = 3, compares = 25, swaps = 48

Answer 3

神奇有用的谷歌关键字：QuickSort

例如 google:how fastsort Works 出现了以下解释：http://www.angelfire.com/pq/jamesbarbetti/articles/sorting/001a_HowQuicksortWorks。 htm等等。

本质上，该代码对指定的左边界和右边界之间的元素应用了快速排序的变体。

对于您已识别的行：

1. 将中间元素与第一个（左侧）元素交换。 它将成为“枢轴”。

2. 跟踪较大和较小元素之间的边界。 这是枢轴所属的位置。

3. 对于第一个元素之后的每个元素，
4. 如果它小于枢轴，

5. 将其移动到第一个较大元素之前。

6. 将枢轴移回原位。

7. 递归地将 qsort 应用于枢轴之前的元素。 （较小的）

8. 递归地将 qsort 应用于枢轴之后的元素。 （较大的）

尝试自己将代码应用到数字列表中，看看它是否更有意义......

Answer 4

您的代码中有一个错误，末尾的行：

qsort(v, left, last - 1); [7]
qsort(v, last + 1, right);  [8]

应该是：

qsort(v, left, last - 1, comp); [7]
qsort(v, last + 1, right, comp);  [8]

或者我遗漏了什么？

此外，重用标准库的名称是一种不好的风格，特别是当新函数的签名与库中的签名不同时。
标准库的函数 qsort 具有以下原型：

 void  qsort(void  *base,  size_t  nel,  size_t  width,   int (*compar)(const void *, const void *));

如果您的程序有点大（多个目标文件），这可能会产生有趣的错误。 想象一下另一个模块调用标准 qsort 函数，但当您使用兼容的签名但具有不同的语义重新定义它时，您会遇到意外的错误。

Answer 5

嗨，我做了第 87 页的示例。也许有人会从中理解。 但在使用此代码之前，请参阅 quicksort

/**
 * qsort.c
 * Quick sort using recursion
 */

#include <stdio.h>

void qsort(int v[], int left, int right);

int main()
{
    int v[] = {9, 3, 4, 6, 7, 3, 1};
    qsort(v, 0, 6);

    int i;

    for (i = 0; i < 7; i++)
        printf(" %d ", v[i]);

    printf("\n");

    return 0;
}

void qsort(int v[], int left, int right)
{
    int i, last; /* last is pivot */

    void swap(int v[], int i, int j);

    if (left >= right)
        return;

    swap(v, left, (left + right) / 2); // swap mid element to front
    last = left;                       // set this position as pivot

    for (i = left + 1; i <= right; i++) { 
        /*loop through every other element 
          swap elements less than pivot i.e bigger to right, smaller to left
        */ 

        if (v[i] < v[left])
            swap(v, ++last, i);     // when swapping lesser element, record
                                    // where our pivot moves
        /*
           we don't swap elements that are bigger than pivot, and are to right.
           However we swap elements those are less than pivot.
           With ++pivot we are essentially going to find out, where our
           pivot will fit to be at the position, where all the elements
           before it are less than it and all after it greater.
        */
    }

    // swap left(our pivot) to last(where pivot must go
    // i.e all elements before pivot are less than it
    // and all elements above it are greater
    // remember they are lesser and greater 
    // but may not be sorted still
    // this is called partition
    swap(v, left, last);

    // Do same(qsort) for all the elements before our pivot
    // and above our pivot
    qsort(v, left, last - 1);   // last is our pivot position
    qsort(v, last + 1, right);

    // Each of above two qsort will use middle element as pivot and do
    // what we did above, because same code will be executed by recursive
    // functions

}                                       

void swap(int v[], int i, int j)
{
    int temp;

    temp = v[i];
    v[i] = v[j];
    v[j] = temp;
}

最重要的部分是枢轴（将一只脚放在适当的位置，同时可以自由移动另一只脚）。 我们选择中间元素作为枢轴，将其置于前面，并将其与所有其他元素进行比较。 如果它们小于我们的主元，我们交换它们并仅增加我们的主元位置（注意我们的主元元素仍然位于第一位置）。 完成循环后，我们将枢轴元素（首先）带到这个位置（枢轴位置）。 循环结束后，pivot 之前的所有元素都小于pivot，而pivot 之上的所有元素都大于pivot。 第一次循环时它们没有排序。 因此，您必须再次对枢轴下方和枢轴上方的所有元素递归应用相同的排序算法来对它们进行排序。