[经典算法] 归并排序

合并排序伪代码(使用哨兵)：
merge(A,p,q,r):
    n1 <—— q-p+1
    n2 <—— r-q
    create array L[0,n1] and R[0,n2]
    for i <—— 0 to n1-1
        do L[i] <—— A[p+i]
    for j <—— 0 to n2-1
        do R[j] <—— A[q+j+1]
    L[n1] <—— +∞
    R[n2] <—— +∞
    i <—— 0
    j <—— 0
    for k i <—— p to r
        do if L[i]<=R[j]
            then A[k]  <—— L[i]
                 i <—— i+1
           else A[k] <—— R[j]
                 j <—— j+1
 
//通过调用merge完成排序：
merge_sort(A,p,r)：
    if p<r
       then q <—— [(p+r)/2] //向下取整
          merge_sort(A,p,q) //分治
          merge_sort(A,q+1,r)
          merge(A,p,q,r)    //合并结果

#include <gtest/gtest.h>
#include <algorithm>

using namespace std;

template<typename T>
void Merge(T* data, int low, int mid, int high)
{
    T* tmp = new T[high - low + 1];
    int i = low;
    int j = mid + 1;
    int k = 0;

    // 把较小的数先移到新数组中 
    while (i <= mid && j <= high)
    {
        if (data[i] < data[j])
        {
            tmp[k++] = data[i++];
        }
        else
        {
            tmp[k++] = data[j++];
        }
    }

    // 把左边剩余的数移入数组  
    while (i <= mid)
    {
        tmp[k++] = data[i++];
    }

    // 把右边边剩余的数移入数组
    while (j <= high)
    {
        tmp[k++] = data[j++];
    }

    // 把新数组中的数覆盖nums数组  
    for (int i = 0; i < k; ++i)
    {
        data[i+low] = tmp[i];
    }

    delete[] tmp;
}

template<typename T>
void MergeSort(T* data, int low, int high)
{
    if (low < high)
    {
        int mid = (low + high)/2;
        // 左边
        MergeSort(data, low, mid);
        // 右边 
        MergeSort(data, mid+1, high);
        // 左右归并
        Merge(data, low, mid, high);
    }
}

template<typename T>
static void ShowElem(T& val)
{
    cout << val << " ";
}

template<typename T>
static bool Validate(T* data, int len)
{
    for (int i=0; i < len-1; ++i)
    {
        if (data[i] > data[i+1])
        {
            return false;
        }
    }

    return true;
}

TEST(Algo, tMergeSort)
{
    int d1[] = {2,8,7,1,3,5,6,4};
    MergeSort(d1, 0, 7);
    for_each(d1, d1+8, ShowElem<int>);
    ASSERT_TRUE(Validate(d1,8));
    cout << endl;

    int d2[] = {2};
    MergeSort(d2, 0, 0);
    for_each(d2, d2+1, ShowElem<int>);
    ASSERT_TRUE(Validate(d2,1));
    cout << endl;

    int d3[] = {2,4,5,6,7,5,2,3,5,7,10,111,2,4,5,6,3,4,5};
    MergeSort(d3, 0, 18);
    for_each(d3, d3+19, ShowElem<int>);
    ASSERT_TRUE(Validate(d3,19));
    cout << endl;
}

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