算法导论第三版--插入排序和归并排序

囧，道理很简单，实践起来却没那么简单。因为编程语言的语言元素跟算法描述数据结构并不完全一致。

经过迭代（此处省略800字），补充上对于归并排序对于小数组采用插入排序的代码。

首先是插入排序：

template<typename _InIt, typename _Func>
void __insert_sort(_InIt first, _InIt last, _Func& Func) {
    typedef typename iterator_traits<_InIt>::value_type _ValueType;

    for (_InIt it = first + 1; it != last+1; ++it) {
        _ValueType key = *it;
        _InIt ite = it - 1;
        for (; (ite - first)>=0 && !Func(*ite, key); --ite)
            *(ite + 1) = *ite;
        *(ite + 1) = key;
    }
}

template<typename _InIt, typename _Func>
void insert_sort(_InIt first, _InIt last, _Func& Func) {
    __insert_sort(first, last-1, Func);
}

 然后是普通的归并排序：

template<typename _InIt, typename _Func>
void __merge(_InIt first, _InIt last, _Func& Func) {
    typedef typename iterator_traits<_InIt>::value_type _ValueType;
    vector<_ValueType> lv, rv;
    size_t q = floor((last-first)/2);

    copy(first, first+q+1, back_inserter(lv));
    copy(first+q+1, last+1, back_inserter(rv));

    typename vector<_ValueType>::iterator lit = lv.begin();
    typename vector<_ValueType>::iterator rit = rv.begin();

    _InIt it = first;
    for (; it != last+1; ++it) {
        if (lit == lv.end() || rit == rv.end()) break;
        *it = Func(*lit, *rit) ? *(lit++) : *(rit++);
    }

    for(; lit != lv.end() && it != last+1; ++lit, ++it) *it = *lit;
    for(; rit != rv.end() && it != last+1; ++rit, ++it) *it = *rit;
}

template<typename _InIt, typename _Func>
void __merge_sort(_InIt first, _InIt last, _Func& Func) {
    if (last - first > 0) {
        size_t q = floor((last - first)/2);
        __merge_sort(first, first+q, Func);
        __merge_sort(first+q+1, last, Func);
        __merge(first, last, Func);
    }
}

template<typename _InIt, typename _Func>
void merge_sort(_InIt first, _InIt last, _Func& Func) {
    __merge_sort(first, last-1, Func);
}

归并排序中的小数组采用插入排序：

template<typename _InIt, typename _Func>
void __merge_sort(_InIt first, _InIt last, int k, _Func& Func) {
    if (last - first > 0) {
        int q = floor((last - first)/2);
        if (q <= k) {
            __insert_sort(first, last, Func);
        } else {
            __merge_sort(first, first+q, k, Func);
            __merge_sort(first+q+1, last, k, Func);
            __merge(first, last, Func);
        }
    }
}

template<typename _InIt, typename _Func>
void merge_sort(_InIt first, _InIt last, int k, _Func& Func) {
    __merge_sort(first, last-1, k, Func);
}

测试函数：

#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>

using namespace std;

template<typename T>
void print(const vector<T>& v) {
    for(vector<int>::const_iterator it=v.begin(); it != v.end(); it++)
           cout << *it << " ";
        cout << endl;
}

template<typename _InIt>
void print(_InIt first, _InIt last) {
    for(vector<int>::const_iterator it=first; it != last; it++)
        cout << *it << " ";
    cout << endl;
}

int main() {
    int lst[] = {1,5,2,6,3,7,4,8};
    vector<int> v(lst, lst+8);

    less<int> l;
    insert_sort(v.begin(), v.end(), l);
    print(v);

    int lst2[] = {2,4,5,7,1,2,3,6};
    vector<int> v2(lst2, lst2+8);
    less_equal<int> lq;

    merge_sort(v2.begin(), v2.end(), v2.size()/2, lq);
    //merge_sort(v2.begin(), v2.end(), lq);
    print(v2);

    return 0;
}