# 3-Way快速排序（荷兰国旗算法）算法详细代码实现

2021年3月21日17:26:08 发表评论 915 次浏览

## 本文概述

3种方式的快速排序的想法是处理枢轴的所有事件, 它基于

``````In 3 Way QuickSort, an array arr[l..r] is divided in 3 parts:
a) arr[l..i] elements less than pivot.
b) arr[i+1..j-1] elements equal to pivot.
c) arr[j..r] elements greater than pivot.``````

## C ++

``````// C++ program for 3-way quick sort
#include <bits/stdc++.h>
using namespace std;

/* This function partitions a[] in three parts
a) a[l..i] contains all elements smaller than pivot
b) a[i+1..j-1] contains all occurrences of pivot
c) a[j..r] contains all elements greater than pivot */
void partition( int a[], int l, int r, int & i, int & j)
{
i = l - 1, j = r;
int p = l - 1, q = r;
int v = a[r];

while ( true ) {
// From left, find the first element greater than
// or equal to v. This loop will definitely
// terminate as v is last element
while (a[++i] < v)
;

// From right, find the first element smaller than
// or equal to v
while (v < a[--j])
if (j == l)
break ;

// If i and j cross, then we are done
if (i >= j)
break ;

// Swap, so that smaller goes on left greater goes
// on right
swap(a[i], a[j]);

// Move all same left occurrence of pivot to
// beginning of array and keep count using p
if (a[i] == v) {
p++;
swap(a``````, a[i]);
}

// Move all same right occurrence of pivot to end of
// array and keep count using q
if (a[j] == v) {
q--;
swap(a[j], a[q]);
}
}

// Move pivot element to its correct index
swap(a[i], a[r]);

// Move all left same occurrences from beginning
j = i - 1;
for ( int k = l; k < p; k++, j--)
swap(a[k], a[j]);

// Move all right same occurrences from end
i = i + 1;
for ( int k = r - 1; k > q; k--, i++)
swap(a[i], a[k]);
}

// 3-way partition based quick sort
void quicksort( int a[], int l, int r)
{
if (r <= l)
return ;

int i, j;

// Note that i and j are passed as reference
partition(a, l, r, i, j);

// Recur
quicksort(a, l, j);
quicksort(a, i, r);
}

// A utility function to print an array
void printarr( int a[], int n)
{
for ( int i = 0; i < n; ++i)
printf ( "%d  " , a[i]);
printf ( "\n" );
}

// Driver code
int main()
{
int a[] = { 4, 9, 4, 4, 1, 9, 4, 4, 9, 4, 4, 1, 4 };
int size = sizeof (a) / sizeof ( int );

// Function Call
printarr(a, size);
quicksort(a, 0, size - 1);
printarr(a, size);
return 0;
}``````

## C#

``````// C# program for 3-way quick sort
using System;

class GFG {
// A function which is used to swap values
static void swap<T>( ref T lhs, ref T rhs)
{
T temp;
temp = lhs;
lhs = rhs;
rhs = temp;
}
/* This function partitions a[] in three parts
a) a[l..i] contains all elements smaller than pivot
b) a[i+1..j-1] contains all occurrences of pivot
c) a[j..r] contains all elements greater than pivot
*/
public static void partition( int [] a, int l, int r, ref int i, ref int j)
{
i = l - 1;
j = r;
int p = l - 1, q = r;
int v = a[r];

while ( true ) {
// From left, find the first element greater
// than or equal to v. This loop will definitely
// terminate as v is last element
while (a[++i] < v)
;

// From right, find the first element smaller
// than or equal to v
while (v < a[--j])
if (j == l)
break ;

// If i and j cross, then we are done
if (i >= j)
break ;

// Swap, so that smaller goes on left greater
// goes on right
swap( ref a[i], ref a[j]);

// Move all same left occurrence of pivot to
// beginning of array and keep count using p
if (a[i] == v) {
p++;
swap( ref a``````, ref a[i]);
}

// Move all same right occurrence of pivot to
// end of array and keep count using q
if (a[j] == v) {
q--;
swap( ref a[j], ref a[q]);
}
}

// Move pivot element to its correct index
swap( ref a[i], ref a[r]);

// Move all left same occurrences from beginning
j = i - 1;
for ( int k = l; k < p; k++, j--)
swap( ref a[k], ref a[j]);

// Move all right same occurrences from end
i = i + 1;
for ( int k = r - 1; k > q; k--, i++)
swap( ref a[i], ref a[k]);
}

// 3-way partition based quick sort
public static void quicksort( int [] a, int l, int r)
{
if (r <= l)
return ;

int i = 0, j = 0;

// Note that i and j are passed as reference
partition(a, l, r, ref i, ref j);

// Recur
quicksort(a, l, j);
quicksort(a, i, r);
}

// A utility function to print an array
public static void printarr( int [] a, int n)
{
for ( int i = 0; i < n; ++i)
Console.Write(a[i] + " " );
Console.Write( "\n" );
}

// Driver code
static void Main()
{
int [] a = { 4, 9, 4, 4, 1, 9, 4, 4, 9, 4, 4, 1, 4 };
int size = a.Length;

// Function Call
printarr(a, size);
quicksort(a, 0, size - 1);
printarr(a, size);
}
// This code is contributed by DrRoot_
}``````

``````4  9  4  4  1  9  4  4  9  4  4  1  4
1  1  4  4  4  4  4  4  4  4  9  9  9``````

## C ++

``````// C++ program for 3-way quick sort
#include <bits/stdc++.h>
using namespace std;

void swap( int * a, int * b)
{
int temp = *a;
*a = *b;
*b = temp;
}

// A utility function to print an array
void printarr( int a[], int n)
{
for ( int i = 0; i < n; ++i)
printf ( "%d " , a[i]);
printf ( "\n" );
}

/* This function partitions a[] in three parts
a) a[l..i] contains all elements smaller than pivot
b) a[i+1..j-1] contains all occurrences of pivot
c) a[j..r] contains all elements greater than pivot */

// It uses Dutch National Flag Algorithm
void partition( int a[], int low, int high, int & i, int & j)
{
// To handle 2 elements
if (high - low <= 1) {
if (a[high] < a[low])
swap(&a[high], &a[low]);
i = low;
j = high;
return ;
}

int mid = low;
int pivot = a[high];
while (mid <= high) {
if (a[mid] < pivot)
swap(&a[low++], &a[mid++]);
else if (a[mid] == pivot)
mid++;
else if (a[mid] > pivot)
swap(&a[mid], &a[high--]);
}

// update i and j
i = low - 1;
j = mid; // or high+1
}

// 3-way partition based quick sort
void quicksort( int a[], int low, int high)
{
if (low >= high) // 1 or 0 elements
return ;

int i, j;

// Note that i and j are passed as reference
partition(a, low, high, i, j);

// Recur two halves
quicksort(a, low, i);
quicksort(a, j, high);
}

// Driver Code
int main()
{
int a[] = { 4, 9, 4, 4, 1, 9, 4, 4, 9, 4, 4, 1, 4 };
// int a[] = {4, 39, 54, 14, 31, 89, 44, 34, 59, 64, 64, // 11, 41}; int a[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
// int a[] = {91, 82, 73, 64, 55, 46, 37, 28, 19, 10};
// int a[] = {4, 9, 4, 4, 9, 1, 1, 1};
int size = sizeof (a) / sizeof ( int );

// Function Call
printarr(a, size);
quicksort(a, 0, size - 1);
printarr(a, size);
return 0;
}``````

## C#

``````// C# program for 3-way quick sort
using System;

class GFG {
// A function which is used to swap values
static void swap<T>( ref T lhs, ref T rhs)
{
T temp;
temp = lhs;
lhs = rhs;
rhs = temp;
}

// A utility function to print an array
public static void printarr( int [] a, int n)
{
for ( int i = 0; i < n; ++i)
Console.Write(a[i] + " " );
Console.Write( "\n" );
}

/* This function partitions a[] in three parts
a) a[l..i] contains all elements smaller than pivot
b) a[i+1..j-1] contains all occurrences of pivot
c) a[j..r] contains all elements greater than pivot */

// It uses Dutch National Flag Algorithm
public static void partition( int [] a, int low, int high, ref int i, ref int j)
{
// To handle 2 elements
if (high - low <= 1) {
if (a[high] < a[low])
swap( ref a[high], ref a[low]);
i = low;
j = high;
return ;
}

int mid = low;
int pivot = a[high];
while (mid <= high) {
if (a[mid] < pivot)
swap( ref a[low++], ref a[mid++]);
else if (a[mid] == pivot)
mid++;
else if (a[mid] > pivot)
swap( ref a[mid], ref a[high--]);
}

// update i and j
i = low - 1;
j = mid; // or high+1
}

// 3-way partition based quick sort
public static void quicksort( int [] a, int low, int high)
{
if (low >= high) // 1 or 0 elements
return ;

int i = 0, j = 0;

// Note that i and j are passed as reference
partition(a, low, high, ref i, ref j);

// Recur two halves
quicksort(a, low, i);
quicksort(a, j, high);
}

// Driver code
static void Main()
{
int [] a = { 4, 9, 4, 4, 1, 9, 4, 4, 9, 4, 4, 1, 4 };
// int[] a = {4, 39, 54, 14, 31, 89, 44, 34, 59, 64, // 64, 11, 41}; int[] a = {1, 2, 3, 4, 5, 6, 7, 8, 9, // 10}; int[] a = {91, 82, 73, 64, 55, 46, 37, 28, // 19, 10}; int[] a = {4, 9, 4, 4, 9, 1, 1, 1};
int size = a.Length;

// Function Call
printarr(a, size);
quicksort(a, 0, size - 1);
printarr(a, size);
}
// This code is contributed by DrRoot_
}``````

``````4 9 4 4 1 9 4 4 9 4 4 1 4
1 1 4 4 4 4 4 4 4 4 9 9 9``````

http://algs4.cs.princeton.edu/lectures/23DemoPartitioning.pdf

http://www.sorting-algorithms.com/quick-sort-3-way