在简单的QuickSort算法中,我们选择一个元素作为枢轴,围绕枢轴对数组进行分区,然后在枢轴的左右两侧递归获得子数组。
考虑具有许多冗余元素的阵列。例如,{1、4、2、4、2、4、1、2、4、1、2、2、2、2、4、1、4、4、4}。如果在“简单快速排序”中选择4作为枢轴,我们将只修复一个4并递归处理剩余的事件。
3种方式的快速排序的想法是处理所有出现的枢轴,并且基于荷兰国旗算法。
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.
下面是上述算法的实现。
C++
// C++ program for 3-way quick sort
#include
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[p], 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
// to adjacent to arr[i]
j = i - 1;
for (int k = l; k < p; k++, j--)
swap(a[k], a[j]);
// Move all right same occurrences from end
// to adjacent to arr[i]
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;
}
Java
// Java program for 3-way quick sort
import java.util.*;
class GFG
{
static int i, j;
/* 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 */
static void partition(int a[], int l, int r)
{
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
int temp = a[i];
a[i] = a[j];
a[j] = temp;
// Move all same left occurrence of pivot to
// beginning of array and keep count using p
if (a[i] == v) {
p++;
temp = a[i];
a[i] = a[p];
a[p] = temp;
}
// Move all same right occurrence of pivot to end of
// array and keep count using q
if (a[j] == v) {
q--;
temp = a[q];
a[q] = a[j];
a[j] = temp;
}
}
// Move pivot element to its correct index
int temp = a[i];
a[i] = a[r];
a[r] = temp;
// Move all left same occurrences from beginning
// to adjacent to arr[i]
j = i - 1;
for (int k = l; k < p; k++, j--)
{
temp = a[k];
a[k] = a[j];
a[j] = temp;
}
// Move all right same occurrences from end
// to adjacent to arr[i]
i = i + 1;
for (int k = r - 1; k > q; k--, i++)
{
temp = a[i];
a[i] = a[k];
a[k] = temp;
}
}
// 3-way partition based quick sort
static void quicksort(int a[], int l, int r)
{
if (r <= l)
return;
i = 0; j = 0;
// Note that i and j are passed as reference
partition(a, l, r);
// Recur
quicksort(a, l, j);
quicksort(a, i, r);
}
// A utility function to print an array
static void printarr(int a[], int n)
{
for (int i = 0; i < n; ++i)
System.out.printf("%d ", a[i]);
System.out.printf("\n");
}
// Driver code
public static void main(String[] args)
{
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 Rajput-Ji
C#
// C# program for 3-way quick sort
using System;
class GFG {
// A function which is used to swap values
static void swap(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[p], 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
// to adjacent to arr[i]
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
// to adjacent to arr[i]
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_
}
C++
// C++ program for 3-way quick sort
#include
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(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_
}
输出
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
感谢Utkarsh建议上述实现。
使用荷兰国旗算法的另一种实现
C++
// C++ program for 3-way quick sort
#include
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(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_
}
输出
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