最小（大）堆作为一个二叉树结构，广泛应用于最值维护问题。其时间复杂度相对于最小值查找来说，能够从O(n)降低到O(logn)。这里，我们介绍基于vector和C++标准库的带键值最小堆实现。
首先需要引入相关的头文件：
# include <vector>
# include <functional>
# include <algorithm>如果是不带键值的最小堆，比较容易实现。
vector<int> minList;
make_heap(minList.begin(), minList.end(), greater<int>());
//minlist变成最小堆
//堆更新,将vector的最有一个值，加入到已经建堆的vector里
minlist.push_back(9);
push_heap(minlist.begin(), minlist.end(), great<int>());
//堆弹出,将堆的根节点弹出到vector的最后，并弹出
pop_heap(minlist.begin(), minlist.end(), great<int>());
minlist.pop_back();在实际应用中，数据往往是以键值的形式进行处理的。除了进行处理比较值外，还有对应的键。我们希望将键值做为一对信息进行处理。这里，就要引入Pair<>数据类型。
vector<pair<double, int>> minKeyHeap;
minKeyHeap.push_back(make_pair(distance_i, index_i));
make_heap(minKeyHeap.begin(), minKeyHeap.end(), greater<pair<double, char>>());类似于sort，比较方法也能够被重写，参照如下格式。
// TEMPLATE STRUCT greater
template<class _Ty>
struct greater : public binary_function<_Ty, _Ty, bool>
{ // functor for operator>
bool operator()(const _Ty& _Left, const _Ty& _Right) const
{ // apply operator> to operands
return (_Left > _Right);
}
};
// TEMPLATE STRUCT less
template<class _Ty>
struct less : public binary_function<_Ty, _Ty, bool>
{ // functor for operator<
bool operator()(const _Ty& _Left, const _Ty& _Right) const
{ // apply operator< to operands
return (_Left < _Right);
}
};这样我们就得到了对于键值数据的最小堆。这里给一个代码示例：（我们修改了最小堆的比较运算符，使得变成基于char比较的最大堆）
#pragma once
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <string>
#include <vector>
# include <functional>
# include <algorithm>
using namespace std;
// TEMPLATE STRUCT greater
template<class _Ty>
struct greaterNew: public binary_function<pair<double, char>, pair<double, char>, bool>
{ // functor for operator>
bool operator()(pair<double, char> p1, pair<double, char> p2) const
{ // apply operator> to operands
return (p1.second < p2.second);
}
};
void main() {
pair<double, char> p1;
p1.first = 0.12;
p1.second = 'd';
pair<double, char> p2;
p2.first = 0.22;
p2.second = 'c';
pair<double, char> p3;
p3.first = 0.11;
p3.second = 'b';
vector<pair<double, char>> minKeyHeap;
minKeyHeap.push_back(p1);
minKeyHeap.push_back(p2);
minKeyHeap.push_back(p3);
cout << "original vector"<<endl;
for (int i = 0; i < minKeyHeap.size(); i++) {
cout << minKeyHeap[i].first <<","<< minKeyHeap[i].second << endl;
}
cout << "default min-heap"<<endl;
make_heap(minKeyHeap.begin(), minKeyHeap.end(), greater<pair<double, char>>());
for (int i = 0; i < minKeyHeap.size(); i++) {
cout << minKeyHeap[i].first << "," << minKeyHeap[i].second << endl;
}
cout << "design min-heap"<<endl;
make_heap(minKeyHeap.begin(), minKeyHeap.end(), greaterNew<pair<double, char>>());
for (int i = 0; i < minKeyHeap.size(); i++) {
cout << minKeyHeap[i].first << "," << minKeyHeap[i].second << endl;
}
}输出：
original vector
0.12, d
0.22, c
0.11, b
default min-heap
0.11, b
0.22, c
0.12, d
design min-heap
0.12, d
0.22, c
0.11, b