排序-005-Merge-Sort-03-Bottom-Up

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本文深入解析归并排序算法，包括自顶向下与自底向上的实现方式，对比两种方法的性能，并通过具体代码示例展示如何优化归并排序。特别关注了在处理大规模数据和近乎有序数组时的效率提升。

MergeSort.h

#ifndef INC_04_MERGE_SORT_BOTTOM_UP_MERGESORT_H
#define INC_04_MERGE_SORT_BOTTOM_UP_MERGESORT_H

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

using namespace std;


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

    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 ++;}
    }
}

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

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

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

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

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

main.cpp

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


using namespace std;

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

//    for( int sz = 1; sz <= n ; sz += sz )
//        for( int i = 0 ; i < n ; i += sz+sz )
//            // 对 arr[i...i+sz-1] 和 arr[i+sz...i+2*sz-1] 进行归并
//            __merge(arr, i, i+sz-1, min(i+sz+sz-1,n-1) );

    // Merge Sort Bottom Up 优化
    for( int i = 0 ; i < n ; i += 16 )
        insertionSort(arr,i,min(i+15,n-1));

    for( int sz = 16; sz <= n ; sz += sz )
        for( int i = 0 ; i < n - sz ; i += sz+sz )
            if( arr[i+sz-1] > arr[i+sz] )
                __merge(arr, i, i+sz-1, min(i+sz+sz-1,n-1) );
}


int main() {

    int n = 1000000;

    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("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Merge Sort Bottom Up", mergeSortBU, arr2, n);

    delete(arr1);
    delete(arr2);

    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);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Merge Sort Bottom Up", mergeSortBU, arr2, n);

    delete(arr1);
    delete(arr2);

    return 0;
}