归并排序

归并排序：

#include <iostream>
#include "SortTestHelper.h"
#include "InsertionSort.h"

using namespace std;


// 将arr[l...mid]和arr[mid+1...r]两部分进行归并
template<typename T>
void __merge(T arr[], int l, int mid, int r) {

    // 经测试,传递aux数组的性能效果并不好
    T aux[r - l + 1];
    for (int i = l; i <= r; i++)
        aux[i - l] = arr[i];

    int i = l, j = mid + 1;
    for (int k = l; k <= r; k++) {

        if (i > mid) {
            arr[k] = aux[j - l];
            j++;
        }
        else if (j > r) {
            arr[k] = aux[i - l];
            i++;
        }
        else if (aux[i - l] < aux[j - l]) {
            arr[k] = aux[i - l];
            i++;
        }
        else {
            arr[k] = aux[j - l];
            j++;
        }
    }
}

// 递归使用归并排序,对arr[l...r]的范围进行排序
template<typename T>
void __mergeSort(T arr[], int l, int r) {

    if (l >= r)
        return;

    int mid = (l + r) / 2;
    __mergeSort(arr, l, mid);
    __mergeSort(arr, mid + 1, r);
    __merge(arr, l, mid, r);
}

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

    __mergeSort(arr, 0, n - 1);
}

int main() {

    int n = 50000;

    // 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);

    SortTestHelper::testSort("Insertion Sort", insertionSort, arr1, n);
    SortTestHelper::testSort("Merge Sort",     mergeSort,     arr2, n);

    delete[] arr1;
    delete[] arr2;

    cout<<endl;


Test for Random Array, size = 50000, random range [0, 50000]
Insertion Sort : 3.173 s
Merge Sort : 0.012 s


    // 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);

    SortTestHelper::testSort("Insertion Sort", insertionSort, arr1, n);
    SortTestHelper::testSort("Merge Sort",     mergeSort,     arr2, n);

    delete(arr1);
    delete(arr2);

Test for Random Nearly Ordered Array, size = 50000, swap time = 100
Insertion Sort : 0.008 s
Merge Sort : 0.008 s


    return 0;
}

归并排序优化：

// 递归使用归并排序,对arr[l...r]的范围进行排序
template<typename T>
void __mergeSort2(T arr[], int l, int r){

    // 对于小规模数组,使用插入排序
    if( r - l <= 15 ){
        insertionSort(arr, l, r);
        return;
    }

    int mid = (l+r)/2;
    __mergeSort2(arr, l, mid);
    __mergeSort2(arr, mid+1, r);
    // 对于arr[mid] <= arr[mid+1]的情况,不进行merge
    // 对于近乎有序的数组非常有效,但是对于一般情况,有一定的性能损失
    if( arr[mid] > arr[mid+1] )
        __merge(arr, l, mid, r);
}

template<typename T>
void mergeSort2(T arr[], int n){
    __mergeSort2( arr , 0 , n-1 );
}

优化后的测试：

int main() {

    int n = 50000;

    // 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("Insertion Sort", insertionSort, arr1, n);
    SortTestHelper::testSort("Merge Sort",     mergeSort,     arr2, n);
    SortTestHelper::testSort("Merge Sort 2",   mergeSort2,    arr3, n);

Test for Random Array, size = 50000, random range [0, 50000]
Insertion Sort : 3.181 s
Merge Sort : 0.012 s
Merge Sort 2 : 0.011 s

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

    cout<<endl;


    // 测试2 测试近乎有序的数组
    int swapTimes = 10;
    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("Insertion Sort", insertionSort, arr1, n);
    SortTestHelper::testSort("Merge Sort",     mergeSort,     arr2, n);
    SortTestHelper::testSort("Merge Sort 2",   mergeSort2,    arr3, n);

Test for Random Nearly Ordered Array, size = 50000, swap time = 10
Insertion Sort : 0.001 s
Merge Sort : 0.007 s
Merge Sort 2 : 0.002 s

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

    return 0;
}