归并排序

归并的意思是: 先递归拆分排序，再合并每个小的（相临的）数组。

下面是代码(C++14)

#include <iostream>
#include <vector>
#include <deque>
#include <iterator>
#include <algorithm>

using std::cout;
using std::endl;
using std::copy;
using std::vector;
using std::deque;
using std::ostream_iterator;

template <typename OS, typename C>
OS & Print(OS & os, const C & c)
{
    using T = typename C::value_type;
    copy(begin(c), end(c), ostream_iterator<T>(os, "	"));
    return os;
}

template <typename C, typename ST = typename C::size_type>
void Merge(C & c, ST first, ST middle, ST last)
{
    ST  f = first,
        m = middle + 1,
        k = 0;

    C temp (last - first);

    // 合并的时候排序
    while (f <= middle && m <= last)
    {
        if (c[f] < c[m])
        {
            temp[k++] = c[f++];
        }
        else
        {
            temp[k++] = c[m++];
        }
    }

    // 两段区间, 谁还没复制完, 继续
    while (f <= middle)
    {
        temp[k++] = c[f++];
    }

    while (m <= last)
    {
        temp[k++] = c[m++];
    }

    // 把 temp 复制回 c, 覆盖 c 中的[first, last] 区域
    // (因为 temp 就是 c 中这个区域 已经排序的值)
    copy_n(temp.begin(), k, c.begin() + first);
}

// 排序实际上是最简单的, 也就是个递归操作: 分别对前后两部分进行排序, 然后再合并
template <typename C, typename ST = typename C::size_type>
void Sort(C & c, ST first, ST last)
{
    if (first < last)
    {
        ST mid = (first + last) / 2;
        Sort(c, first, mid);
        Sort(c, mid + 1, last);
        Merge(c, first, mid, last);
    }
}

int main()
{
    vector<int> vi {10, 9, 8, 15, 7, 24, 5, 4, 2, 95};
    Print(cout, vi) << endl;
    Sort(vi, (vector<int>::size_type)0, vi.size() - 1);
    Print(cout, vi) << endl << "--------------" << endl;

    deque<double> di {1.0, 9.4, 3.88, 1.5, 7.8, 2.4, 5.9, 4.2, 2.8, 9.5};
    Print(cout, di) << endl;
    Sort(di, (deque<int>::size_type)0, vi.size() - 1);
    Print(cout, di) << endl << "--------------" << endl;
}