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heap
-------------------------------------------------------------------------binary heap 是一种全然二叉树。
隐式表示法：以 array 表述 tree。
小技巧：将 array 的 #0 元素保留。则第 i 个元素的左右子节点各自是 2i 和 2i + 1，
父节点是i/2 --> STL 里没有採用这样的小技巧
将 array 无法动态改变大小，所以用 vector 替代 array
这个文件中提供了各种堆操作的算法，注意没有 heap 类
图 4-20
演示样例：
#include <vector>
#include <iostream>
#include <iterator>
#include <algorithm>
using namespace std;
void display(const vector<int> &v){
copy(v.begin(), v.end(), ostream_iterator<int>(cout, " "));
cout << endl;
}
int main(){
int ia[] = {0,1,2,3,4,8,9,3,5};
vector<int> ivec(ia, ia + sizeof(ia)/sizeof(int));
make_heap(ivec.begin(),ivec.end());
display(ivec);
ivec.push_back(7);
push_heap(ivec.begin(), ivec.end());
display(ivec);
pop_heap(ivec.begin(), ivec.end());
ivec.pop_back();
display(ivec);
sort_heap(ivec.begin(), ivec.end());
display(ivec);
}源代码：
#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
template <class RandomAccessIterator, class Distance, class T>
void __push_heap(RandomAccessIterator first, Distance holeIndex,
Distance topIndex, T value) {
Distance parent = (holeIndex - 1) / 2; //找到父节点
// 当尚未到达顶端。且父节点小于新值(于是不符合 heap 的次序特性)
while (holeIndex > topIndex && *(first + parent) < value) {
*(first + holeIndex) = *(first + parent); //令洞值为父值
holeIndex = parent; //调整洞号。向上提升至父节点
parent = (holeIndex - 1) / 2; //新洞的父节点
}
*(first + holeIndex) = value; //令洞值为新值。完毕插入操作
}
template <class RandomAccessIterator, class Distance, class T>
inline void __push_heap_aux(RandomAccessIterator first,
RandomAccessIterator last, Distance*, T*) {
__push_heap(first, Distance((last - first) - 1), Distance(0),
T(*(last - 1)));
}
/*调用此函数时，新元素应已置于底部容器的最尾端
--> 什么时候置的？
--> stl_heap 不正确外开放，仅仅在 STL 内部使用，使用 push_heap 的其它 STL 程序应该注意在调用
push_heap 函数前，将新元素置于 heap 底部容器的最尾端
*/
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;
}
//STL 里非常多这样的函数体里直接调用还有一个函数的函数。感觉这样不太好。添加了堆栈的开销，
//为什么不直接就调用里面那个函数呢
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);
}
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));
}
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;
while (secondChild < len) {
if (*(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);
}
template <class RandomAccessIterator, class T, class Distance>
inline void __pop_heap(RandomAccessIterator first, RandomAccessIterator last,
RandomAccessIterator result, T value, Distance*) {
*result = *first;
__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 操作的结果应该底部容器的第一个元素
__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; //洞节点的右子节点
while (secondChild < len) { //当还有左、右子节点的时候
if (comp(*(first + secondChild), *(first + (secondChild - 1))))
secondChild--;
*(first + holeIndex) = *(first + secondChild); //令较大值为洞值
holeIndex = secondChild; //令洞号下移至较大子节点处
secondChild = 2 * (secondChild + 1); //找出新洞节点的子节点
}
if (secondChild == len) { //当仅仅有左节点的时候
*(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*) {
//将首值(即要 pop 出来的值)存放在 result 所指处。
*result = *first;
//又一次调整 heap 。 洞号为0。欲调整值为 value
__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);
}
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;
//找出第一个须要重排的子树的头部。以 parent 标示出。
Distance parent = (len - 2)/2;
while (true) {
__adjust_heap(first, parent, len, T(*(first + parent)), comp);
if (parent == 0) return; //走完根节点。就结束了。
parent--; //实际上就是沿着第一个父节点从左到右调整值使父节点的值大于(或小于)两个子节点
}
}
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));
}
template <class RandomAccessIterator>
void sort_heap(RandomAccessIterator first, RandomAccessIterator last) {
//每次运行一次 pop_heap() ，极值被放在尾端
//扣除尾端再运行一次 pop_heap()。次极值又被放在新尾端
//一直这样下去，最后就可以得到排序结果
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:
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