在里面 简单快速排序 算法中，我们选择一个元素作为支点，围绕支点对数组进行分区，并在支点的左侧和右侧重现子数组。 考虑一个具有许多冗余元素的数组。例如，{1,4,2,4,2,4,1,2,4,1,2,2,2,2,4,1,4,4}。如果在简单快速排序中选择4作为轴心，我们只修复一个4，并递归处理剩余的事件。 三向快速排序的思想是处理轴的所有出现，并基于 荷兰国旗算法。
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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 <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[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 ( "" ); } // 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( "" ); } // 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<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[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( "" ); } // 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_ } |
Javascript
<script> // javascript program for 3-way quick sort var 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 */ function partition(a , l , r) { i = l - 1; j = r; var p = l - 1, q = r; var 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 var 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 var 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 (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 (k = r - 1; k > q; k--, i++) { temp = a[i]; a[i] = a[k]; a[k] = temp; } } // 3-way partition based quick sort function quicksort(a , l , 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 function printarr(a , n) { for (i = 0; i < n; ++i) document.write( " " + a[i]); document.write( "<br/>" ); } // Driver code var a = [ 4, 9, 4, 4, 1, 9, 4, 4, 9, 4, 4, 1, 4 ]; var size = a.length; // Function Call printarr(a, size); quicksort(a, 0, size - 1); printarr(a, size); // This code contributed by aashish1995 </script> |
Python3
''' This function partitions a[] in three parts a) a[first..start] contains all elements smaller than pivot b) a[start+1..mid-1] contains all occurrences of pivot c) a[mid..last] contains all elements greater than pivot ''' def partition(arr, first, last, start, mid): pivot = arr[last] end = last # Iterate while mid is not greater than end. while (mid[ 0 ] < = end): # Inter Change position of element at the starting if it's value is less than pivot. if (arr[mid[ 0 ]] < pivot): arr[mid[ 0 ]], arr[start[ 0 ]] = arr[start[ 0 ]], arr[mid[ 0 ]] mid[ 0 ] = mid[ 0 ] + 1 start[ 0 ] = start[ 0 ] + 1 # Inter Change position of element at the end if it's value is greater than pivot. elif (arr[mid[ 0 ]] > pivot): arr[mid[ 0 ]], arr[end] = arr[end], arr[mid[ 0 ]] end = end - 1 else : mid[ 0 ] = mid[ 0 ] + 1 # Function to sort the array elements in 3 cases def quicksort(arr,first,last): # First case when an array contain only 1 element if (first > = last): return # Second case when an array contain only 2 elements if (last = = first + 1 ): if (arr[first] > arr[last]): arr[first], arr[last] = arr[last], arr[first] return # Third case when an array contain more than 2 elements start = [first] mid = [first] # Function to partition the array. partition(arr, first, last, start, mid) # Recursively sort sublist containing elements that are less than the pivot. quicksort(arr, first, start[ 0 ] - 1 ) # Recursively sort sublist containing elements that are more than the pivot quicksort(arr, mid[ 0 ], last) # Code Start from here arr = [ 4 , 9 , 4 , 4 , 1 , 9 , 4 , 4 , 9 , 4 , 4 , 1 , 4 ] # Call the quicksort function. quicksort(arr, 0 , len (arr) - 1 ) # print arr after sorting the elements print (arr) |
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
时间复杂性 : O（N*log（N））
其中“N”是给定数组/列表中的元素数
对快速排序函数进行递归调用的平均次数为logn，每次调用该函数时，我们都要遍历给定的数组/列表，这需要O（N）个时间。因此，总时间复杂度为O（N*log（N））。
空间复杂性： O（对数N）
其中“N”是给定数组/列表中的元素数。
幸亏 乌特卡什 感谢您提出上述实施建议。
另一个实现使用 荷兰国旗算法
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 ( "" ); } /* 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( "" ); } /* 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
谢谢 阿迪蒂亚·戈尔 对于这个实现。 参考： http://algs4.cs.princeton.edu/lectures/23DemoPartitioning.pdf http://www.sorting-algorithms.com/quick-sort-3-way 如果您发现任何不正确的地方，或者您想分享有关上述主题的更多信息，请写下评论。
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