STL源码剖析 [容器]（七）[stl_heap.h]
make_heap()、push_heap()、pop_heap()、sort_heap()是主要函数。
建立堆【make_heap(_First, _Last, _Comp)】：默认是建立最大堆的。对int类型，可以在第三个参数传入greater<int>()得到最小堆。
添加数据【push_heap (_First, _Last)】：要先在容器中加入数据，再调用push_heap ()
删除数据【pop_heap(_First, _Last)】：要先调用pop_heap()再在容器中删除数据
堆排序【sort_heap(_First, _Last) 】：排序之后就不再是一个合法的heap了
stl_heap.h源码：
// Filename: stl_heap.h // Comment By: 凝霜 // E-mail: [email protected] // Blog: http://blog.csdn.net/mdl13412 /* * * Copyright (c) 1994 * Hewlett-Packard Company * * Permission to use, copy, modify, distribute and sell this software * and its documentation for any purpose is hereby granted without fee, * provided that the above copyright notice appear in all copies and * that both that copyright notice and this permission notice appear * in supporting documentation. Hewlett-Packard Company makes no * representations about the suitability of this software for any * purpose. It is provided "as is" without express or implied warranty. * * Copyright (c) 1997 * Silicon Graphics Computer Systems, Inc. * * Permission to use, copy, modify, distribute and sell this software * and its documentation for any purpose is hereby granted without fee, * provided that the above copyright notice appear in all copies and * that both that copyright notice and this permission notice appear * in supporting documentation. Silicon Graphics makes no * representations about the suitability of this software for any * purpose. It is provided "as is" without express or implied warranty. */ /* NOTE: This is an internal header file, included by other STL headers. * You should not attempt to use it directly. */ #ifndef __SGI_STL_INTERNAL_HEAP_H #define __SGI_STL_INTERNAL_HEAP_H __STL_BEGIN_NAMESPACE #if defined(__sgi) && !defined(__GNUC__) && (_MIPS_SIM != _MIPS_SIM_ABI32) #pragma set woff 1209 #endif //////////////////////////////////////////////////////////////////////////////// // 注意: push_heap()操作前要保证新添加的元素已经加入到容器末尾!!! //////////////////////////////////////////////////////////////////////////////// // 下面是使用默认比较函数的一个实例, XXX代表需要调整结点的位置 // 执行插入前, 元素已经追加到容器尾, 其值为450, 这里我们只 // 关注其位置, 不表示出其数值 // [500] // | // --------------------------------- // | | // [300] [400] // | | // ----------------------- ----------------------- // | | | | // [200] [270] [350] [240] // | | // ----------- ----------- // | | | | // [150] [130] [120] [XXX] // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 500 | 300 | 400 | 200 | 270 | 350 | 240 | 150 | 130 | 120 | XXX | ...... | end | // -------------------------------------------------------------------------------------------- // // 下面是移动步骤及内存变化 // [500] // | // --------------------------------- // | | // [300] [400] // | | // ----------------------- ----------------------- // | | | | // [200] [XXX]------- [350] [240] // | | | // ----------- ----------- | // | | | | | 调整元素位置 // [150] [130] [120] [270]-- // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 500 | 300 | 400 | 200 | XXX | 350 | 240 | 150 | 130 | 120 | 270 | ...... | end | // -------------------------------------------------------------------------------------------- // // [500] // | // --------------------------------- // | | // [XXX]------------- 交换 [400] // | | | // ----------------------- | ----------------------- // | | | | | // [200] [300]-- [350] [240] // | | // ----------- ----------- // | | | | // [150] [130] [120] [270] // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 500 | XXX | 400 | 200 | 300 | 350 | 240 | 150 | 130 | 120 | 270 | ...... | end | // -------------------------------------------------------------------------------------------- // // 现在满足heap的要求了, 对[XXX]直接赋值即可 // //////////////////////////////////////////////////////////////////////////////// template <class RandomAccessIterator, class Distance, class T> void __push_heap(RandomAccessIterator first, Distance holeIndex, Distance topIndex, T value) { // 首先找出待处理元素的父结点 Distance parent = (holeIndex - 1) / 2; // 判断当前待处理结点是否优先级高于其父结点, 如果是则将其父结点向下移动 // 设置当前结点为父结点位置, 继续, 直到优先级小于父结点或者已经到达heap顶端 while (holeIndex > topIndex && *(first + parent) < value) { *(first + holeIndex) = *(first + parent); holeIndex = parent; parent = (holeIndex - 1) / 2; } // 将找到的合适的位置设置成正确值 *(first + holeIndex) = value; } template <class RandomAccessIterator, class Distance, class T> inline void __push_heap_aux(RandomAccessIterator first, RandomAccessIterator last, Distance*, T*) { // 因为first所指的那个元素不是heap的组成元素, 所以计算距离要减去1 __push_heap(first, Distance((last - first) - 1), Distance(0), T(*(last - 1))); } // 调用此函数前要先把待处理元素追加到容器末尾 template <class RandomAccessIterator> inline void push_heap(RandomAccessIterator first, RandomAccessIterator last) { __push_heap_aux(first, last, distance_type(first), value_type(first)); } template <class RandomAccessIterator, class Distance, class T, class Compare> void __push_heap(RandomAccessIterator first, Distance holeIndex, Distance topIndex, T value, Compare comp) { Distance parent = (holeIndex - 1) / 2; while (holeIndex > topIndex && comp(*(first + parent), value)) { *(first + holeIndex) = *(first + parent); holeIndex = parent; parent = (holeIndex - 1) / 2; } *(first + holeIndex) = value; } template <class RandomAccessIterator, class Compare, class Distance, class T> inline void __push_heap_aux(RandomAccessIterator first, RandomAccessIterator last, Compare comp, Distance*, T*) { __push_heap(first, Distance((last - first) - 1), Distance(0), T(*(last - 1)), comp); } // 这个除了用户自己指定优先级决策判别式外和默认的无区别 template <class RandomAccessIterator, class Compare> inline void push_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp) { __push_heap_aux(first, last, comp, distance_type(first), value_type(first)); } //////////////////////////////////////////////////////////////////////////////// // 注意: pop_heap()操作, 执行完操作后要自己将容器尾元素弹出 //////////////////////////////////////////////////////////////////////////////// // 这里以默认的heap优先级决策来说 // STL采用的是先将待pop的元素复制到heap尾部, 然后将整个heap向上调整 // 这样就会将最后空出一个hole, 将原来最后的元素在这里进行push()操作 // 这就是两个shift_up的过程 // 个人感觉使用使用shift_down的算法更高效, 虽然时间复杂度一样, 但是shift_down // 进行操作的元素会更少, // 之所以用shift_up这可能也是STL设计理念的问题吧, 能复用就不写新的^_^ //////////////////////////////////////////////////////////////////////////////// // 下面是使用默认比较函数的一个实例, 我们要弹出的是优先级最高的元素[500] // 首先要把弹出的元素[500]复制到heap末尾 // 然后进行第一次shift_up, 完成后进行push()操作, 这个就是第二次shift_up了 // // [500] // | // --------------------------------- // | | // [300] [400] // | | // ----------------------- ----------------------- // | | | | // [200] [270] [350] [240] // | | // ----------- ----------- // | | | | // [150] [130] [120] [100] // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 500 | 300 | 400 | 200 | 270 | 350 | 240 | 150 | 130 | 120 | 100 | ...... | end | // -------------------------------------------------------------------------------------------- // // 下面是移动步骤及内存变化 复制 // [500]---------------------------------- // | | // --------------------------------- | // | | | // [300] [400] | // | | | // ----------------------- ----------------------- | // | | | | | // [200] [270] [350] [240] | // | | | // ----------- ----------- | // | | | | | // [150] [130] [120] [500]---------------------------------- // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 500 | 300 | 400 | 200 | 270 | 350 | 240 | 150 | 130 | 120 | 500 | ...... | end | // -------------------------------------------------------------------------------------------- // // [400]----------------------- // | | // --------------------------------- | shift_up // | | | // [300] [400]------- // | | // ----------------------- ----------------------- // | | | | // [200] [270] [350] [240] // | | // ----------- ----------- // | | | | // [150] [130] [120] [500] // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 400 | 300 | 400 | 200 | 270 | 350 | 240 | 150 | 130 | 120 | 500 | ...... | end | // -------------------------------------------------------------------------------------------- // // [400] // | // --------------------------------- // | | shift_up // [300] [350]------------------- // | | | // ----------------------- ----------------------- | // | | | | | // [200] [270] [350] [240] | // | | | | // ----------- ----------- ---------------------------------- // | | | | // [150] [130] [120] [500] // // first last // ↓ ↓ // -------------------------------------------------------------------------------------------- // | Not Use | 400 | 300 | 350 | 200 | 270 | 350 | 240 | 150 | 130 | 120 | 500 | ...... | end | // -------------------------------------------------------------------------------------------- // // 接下来就是push()操作了, 参考前面的push() //////////////////////////////////////////////////////////////////////////////// template <class RandomAccessIterator, class Distance, class T> void __adjust_heap(RandomAccessIterator first, Distance holeIndex, Distance len, T value) { Distance topIndex = holeIndex; Distance secondChild = 2 * holeIndex + 2; // 弹出元素的有子孩 // 调整heap元素位置 while (secondChild < len) { // 选择两个子孩中较大的进行操作, 使用secondChild表示其偏移 if (*(first + secondChild) < *(first + (secondChild - 1))) secondChild--; // 将较大元素向上填充, 并将整体偏移向下调整, 继续调整 *(first + holeIndex) = *(first + secondChild); holeIndex = secondChild; secondChild = 2 * (secondChild + 1); } if (secondChild == len) { *(first + holeIndex) = *(first + (secondChild - 1)); holeIndex = secondChild - 1; } // 这里就是shift_up过程了, 将最初的heap末尾元素向上调整 // 侯捷老师对这里的理解有误, :-), 人非圣贤, 孰能无过, ^_^ __push_heap(first, holeIndex, topIndex, value); } template <class RandomAccessIterator, class T, class Distance> inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last, RandomAccessIterator result, T value, Distance*) { // 将弹出的元素调整到heap末尾, 这个元素需要用户手动弹出 *result = *first; // 去掉末尾哪个弹出的元素, 调整heap __adjust_heap(first, Distance(0), Distance(last - first), value); } template <class RandomAccessIterator, class T> inline void __pop_heap_aux(RandomAccessIterator first, RandomAccessIterator last, T*) { __pop_heap(first, last - 1, last - 1, T(*(last - 1)), distance_type(first)); } template <class RandomAccessIterator> inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last) { __pop_heap_aux(first, last, value_type(first)); } template <class RandomAccessIterator, class Distance, class T, class Compare> void __adjust_heap(RandomAccessIterator first, Distance holeIndex, Distance len, T value, Compare comp) { Distance topIndex = holeIndex; Distance secondChild = 2 * holeIndex + 2; while (secondChild < len) { if (comp(*(first + secondChild), *(first + (secondChild - 1)))) secondChild--; *(first + holeIndex) = *(first + secondChild); holeIndex = secondChild; secondChild = 2 * (secondChild + 1); } if (secondChild == len) { *(first + holeIndex) = *(first + (secondChild - 1)); holeIndex = secondChild - 1; } __push_heap(first, holeIndex, topIndex, value, comp); } template <class RandomAccessIterator, class T, class Compare, class Distance> inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last, RandomAccessIterator result, T value, Compare comp, Distance*) { *result = *first; __adjust_heap(first, Distance(0), Distance(last - first), value, comp); } template <class RandomAccessIterator, class T, class Compare> inline void __pop_heap_aux(RandomAccessIterator first, RandomAccessIterator last, T*, Compare comp) { __pop_heap(first, last - 1, last - 1, T(*(last - 1)), comp, distance_type(first)); } template <class RandomAccessIterator, class Compare> inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp) { __pop_heap_aux(first, last, value_type(first), comp); } // 这个没设么好说的, 参考上面的分析吧 template <class RandomAccessIterator, class T, class Distance> void __make_heap(RandomAccessIterator first, RandomAccessIterator last, T*, Distance*) { if (last - first < 2) return; Distance len = last - first; Distance parent = (len - 2)/2; while (true) { __adjust_heap(first, parent, len, T(*(first + parent))); if (parent == 0) return; parent--; } } template <class RandomAccessIterator> inline void make_heap(RandomAccessIterator first, RandomAccessIterator last) { __make_heap(first, last, value_type(first), distance_type(first)); } template <class RandomAccessIterator, class Compare, class T, class Distance> void __make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp, T*, Distance*) { if (last - first < 2) return; Distance len = last - first; Distance parent = (len - 2)/2; while (true) { __adjust_heap(first, parent, len, T(*(first + parent)), comp); if (parent == 0) return; parent--; } } template <class RandomAccessIterator, class Compare> inline void make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp) { __make_heap(first, last, comp, value_type(first), distance_type(first)); } // 这个能保证heap有序, 其实个人感觉没啥必要, 这样还不如直接用平衡二叉树 template <class RandomAccessIterator> void sort_heap(RandomAccessIterator first, RandomAccessIterator last) { while (last - first > 1) pop_heap(first, last--); } template <class RandomAccessIterator, class Compare> void sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp) { while (last - first > 1) pop_heap(first, last--, comp); } #if defined(__sgi) && !defined(__GNUC__) && (_MIPS_SIM != _MIPS_SIM_ABI32) #pragma reset woff 1209 #endif __STL_END_NAMESPACE #endif /* __SGI_STL_INTERNAL_HEAP_H */ // Local Variables: // mode:C++ // End:
使用例子：
#include <cstdio>
#include <vector>
#include <algorithm>
#include <functional>
using namespace std;
void PrintfVectorInt(vector<int> &vet)
{
for (vector<int>::iterator pos = vet.begin(); pos != vet.end(); pos++)
printf("%d ", *pos);
putchar('\n');
}
int main()
{
const int MAXN = 20;
int a[MAXN];
int i;
for (i = 0; i < MAXN; ++i)
a[i] = rand() % (MAXN * 2);
//动态申请vector 并对vector建堆
vector<int> *pvet = new vector<int>(40);
pvet->assign(a, a + MAXN);
//建堆
make_heap(pvet->begin(), pvet->end());
PrintfVectorInt(*pvet);
//加入新数据 先在容器中加入，再调用push_heap()
pvet->push_back(25);
push_heap(pvet->begin(), pvet->end());
PrintfVectorInt(*pvet);
//删除数据 要先调用pop_heap()，再在容器中删除
pop_heap(pvet->begin(), pvet->end());
pvet->pop_back();
pop_heap(pvet->begin(), pvet->end());
pvet->pop_back();
PrintfVectorInt(*pvet);
//堆排序
sort_heap(pvet->begin(), pvet->end());
PrintfVectorInt(*pvet);
delete pvet;
return 0;
}
heap排序、堆排序、快速排序，归并排序来进行个性能测试：
#include <cstdio>
#include <algorithm>
#include <ctime>
using namespace std;
//------------------------快速排序----------------------------
void quick_sort(int s[], int l, int r)
{
if (l < r)
{
int i = l, j = r, x = s[l];
while (i < j)
{
while(i < j && s[j] >= x) // 从右向左找第一个小于x的数
j--;
if(i < j)
s[i++] = s[j];
while(i < j && s[i] < x) // 从左向右找第一个大于等于x的数
i++;
if(i < j)
s[j--] = s[i];
}
s[i] = x;
quick_sort(s, l, i - 1); // 递归调用
quick_sort(s, i + 1, r);
}
}
//------------------------归并排序----------------------------
//将有二个有序数列a[first...mid]和a[mid...last]合并。
void mergearray(int a[], int first, int mid, int last, int temp[])
{
int i = first, j = mid + 1;
int m = mid, n = last;
int k = 0;
while (i <= m && j <= n)
{
if (a[i] < a[j])
temp[k++] = a[i++];
else
temp[k++] = a[j++];
}
while (i <= m)
temp[k++] = a[i++];
while (j <= n)
temp[k++] = a[j++];
for (i = 0; i < k; i++)
a[first + i] = temp[i];
}
void mergesort(int a[], int first, int last, int temp[])
{
if (first < last)
{
int mid = (first + last) / 2;
mergesort(a, first, mid, temp); //左边有序
mergesort(a, mid + 1, last, temp); //右边有序
mergearray(a, first, mid, last, temp); //再将二个有序数列合并
}
}
bool MergeSort(int a[], int n)
{
int *p = new int[n];
if (p == NULL)
return false;
mergesort(a, 0, n - 1, p);
return true;
}
//------------------------堆排序---------------------------
inline void Swap(int &a, int &b)
{
int c = a;
a = b;
b = c;
}
//建立最小堆
// 从i节点开始调整,n为节点总数 从0开始计算 i节点的子节点为 2*i+1, 2*i+2
void MinHeapFixdown(int a[], int i, int n)
{
int j, temp;
temp = a[i];
j = 2 * i + 1;
while (j < n)
{
if (j + 1 < n && a[j + 1] < a[j]) //在左右孩子中找最小的
j++;
if (a[j] >= temp)
break;
a[i] = a[j]; //把较小的子结点往上移动,替换它的父结点
i = j;
j = 2 * i + 1;
}
a[i] = temp;
}
//建立最小堆
void MakeMinHeap(int a[], int n)
{
for (int i = n / 2 - 1; i >= 0; i--)
MinHeapFixdown(a, i, n);
}
void MinheapsortTodescendarray(int a[], int n)
{
for (int i = n - 1; i >= 1; i--)
{
Swap(a[i], a[0]);
MinHeapFixdown(a, 0, i);
}
}
const int MAXN = 5000000;
int a[MAXN];
int b[MAXN], c[MAXN], d[MAXN];
int main()
{
int i;
srand(time(NULL));
for (i = 0; i < MAXN; ++i)
a[i] = rand() * rand(); //注rand()产生的数在0到0x7FFF之间
for (i = 0; i < MAXN; ++i)
d[i] = c[i] = b[i] = a[i];
clock_t ibegin, iend;
printf("--当前数据量为%d--By MoreWindows(http://blog.csdn.net/MoreWindows)--\n", MAXN);
//快速排序
printf("快速排序: ");
ibegin = clock();
quick_sort(a, 0, MAXN - 1);
iend = clock();
printf("%d毫秒\n", iend - ibegin);
//归并排序
printf("归并排序: ");
ibegin = clock();
MergeSort(b, MAXN);
iend = clock();
printf("%d毫秒\n", iend - ibegin);
//堆排序
printf("堆排序: ");
ibegin = clock();
MakeMinHeap(c, MAXN);
MinheapsortTodescendarray(c, MAXN);
iend = clock();
printf("%d毫秒\n", iend - ibegin);
//STL中的堆排序
printf("STL中的堆排序: ");
ibegin = clock();
make_heap(d, d + MAXN);
sort_heap(d, d + MAXN);
iend = clock();
printf("%d毫秒\n", iend - ibegin);
return 0;
}