排序-006-Quick-Sort-04-Three-Ways

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本文深入探讨了三种快速排序算法的实现，包括基本快速排序、改进版快速排序和三路快速排序。通过对比不同场景下（如随机数组、近乎有序数组、大量重复元素数组）的排序效率，展示了各种算法的优劣。特别地，三路快速排序针对大量重复元素的情况进行了优化，提高了排序效率。

QuickSort.h


#ifndef INC_07_QUICK_SORT_THREE_WAYS_QUICKSORT_H
#define INC_07_QUICK_SORT_THREE_WAYS_QUICKSORT_H

#include <iostream>
#include <ctime>
#include <algorithm>
#include "InsertionSort.h"

using namespace std;


template <typename T>
int _partition(T arr[], int l, int r){

    swap( arr[l] , arr[rand()%(r-l+1)+l] );

    T v = arr[l];
    int j = l;
    for( int i = l + 1 ; i <= r ; i ++ )
        if( arr[i] < v ){
            j ++;
            swap( arr[j] , arr[i] );
        }

    swap( arr[l] , arr[j]);

    return j;
}

template <typename T>
int _partition2(T arr[], int l, int r){

    swap( arr[l] , arr[rand()%(r-l+1)+l] );
    T v = arr[l];
    int i = l+1, j = r;
    while( true ){
        while( i <= r && arr[i] < v )
            i ++;

        while( j >= l+1 && arr[j] > v )
            j --;

        if( i > j )
            break;

        swap( arr[i] , arr[j] );
        i ++;
        j --;
    }

    swap( arr[l] , arr[j]);

    return j;
}

template <typename T>
void _quickSort(T arr[], int l, int r){

//    if( l >= r )
//        return;
    if( r - l <= 15 ){
        insertionSort(arr,l,r);
        return;
    }

    int p = _partition2(arr, l, r);
    _quickSort(arr, l, p-1 );
    _quickSort(arr, p+1, r);
}

template <typename T>
void quickSort(T arr[], int n){

    srand(time(NULL));
    _quickSort(arr, 0, n-1);
}

#endif //INC_07_QUICK_SORT_THREE_WAYS_QUICKSORT_H

InsertionSort.h

#ifndef INC_08_QUICK_SORT_THREE_WAYS_INSERTIONSORT_H
#define INC_08_QUICK_SORT_THREE_WAYS_INSERTIONSORT_H

#include <iostream>
#include <algorithm>

using namespace std;


template<typename T>
void insertionSort(T arr[], int n){

    for( int i = 1 ; i < n ; i ++ ) {

        T e = arr[i];
        int j;
        for (j = i; j > 0 && arr[j-1] > e; j--)
            arr[j] = arr[j-1];
        arr[j] = e;
    }

    return;
}

// 对arr[l...r]范围的数组进行插入排序
template<typename T>
void insertionSort(T arr[], int l, int r){

    for( int i = l+1 ; i <= r ; i ++ ) {

        T e = arr[i];
        int j;
        for (j = i; j > l && arr[j-1] > e; j--)
            arr[j] = arr[j-1];
        arr[j] = e;
    }

    return;
}

#endif //INC_08_QUICK_SORT_THREE_WAYS_INSERTIONSORT_H

main.cpp

#include <iostream>
#include <algorithm>
#include <ctime>
#include "SortTestHelper.h"
#include "MergeSort.h"
#include "InsertionSort.h"
#include "QuickSort.h"

using namespace std;


template <typename T>
void __quickSort3Ways(T arr[], int l, int r){

    if( r - l <= 15 ){
        insertionSort(arr,l,r);
        return;
    }

    swap( arr[l], arr[rand()%(r-l+1)+l ] );

    T v = arr[l];

    int lt = l;     // arr[l+1...lt] < v
    int gt = r + 1; // arr[gt...r] > v
    int i = l+1;    // arr[lt+1...i) == v
    while( i < gt ){
        if( arr[i] < v ){
            swap( arr[i], arr[lt+1]);
            i ++;
            lt ++;
        }
        else if( arr[i] > v ){
            swap( arr[i], arr[gt-1]);
            gt --;
        }
        else{ // arr[i] == v
            i ++;
        }
    }

    swap( arr[l] , arr[lt] );

    __quickSort3Ways(arr, l, lt-1);
    __quickSort3Ways(arr, gt, r);
}

template <typename T>
void quickSort3Ways(T arr[], int n){

    srand(time(NULL));
    __quickSort3Ways( arr, 0, n-1);
}


int main() {

    int n = 1000000;

    // 测试1 一般性测试
    cout<<"Test for Random Array, size = "<<n<<", random range [0, "<<n<<"]"<<endl;
    int* arr1 = SortTestHelper::generateRandomArray(n,0,n);
    int* arr2 = SortTestHelper::copyIntArray(arr1,n);
    int* arr3 = SortTestHelper::copyIntArray(arr1,n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;

    cout<<endl;


    // 测试2 测试近乎有序的数组
    int swapTimes = 100;
    cout<<"Test for Random Nearly Ordered Array, size = "<<n<<", swap time = "<<swapTimes<<endl;
    arr1 = SortTestHelper::generateNearlyOrderedArray(n,swapTimes);
    arr2 = SortTestHelper::copyIntArray(arr1, n);
    arr3 = SortTestHelper::copyIntArray(arr1, n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;

    cout<<endl;


    // 测试3 测试存在包含大量相同元素的数组
    cout<<"Test for Random Array, size = "<<n<<", random range [0,10]"<<endl;
    arr1 = SortTestHelper::generateRandomArray(n,0,10);
    arr2 = SortTestHelper::copyIntArray(arr1, n);
    arr3 = SortTestHelper::copyIntArray(arr1, n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;

    return 0;
}