STL 源碼剖析 演算法 stl_heap.h

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heap

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binary heap 是一種完全二叉樹。
隱式標記法：以 array 表述 tree。
小技巧：將 array 的 #0 元素保留，則第 i 個元素的左右子節點分別是 2i 和 2i + 1，
父節點是i/2 --> STL 裡沒有採用這種小技巧
將 array 無法動態改變大小，所以用 vector 替代 array
這個檔案裡提供了各種堆操作的演算法，注意沒有 heap 類
圖 4-20


樣本：

#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);}

源碼：

#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#endiftemplate <class RandomAccessIterator, class Distance, class T>void __push_heap(RandomAccessIterator first, Distance holeIndex,                 Distance topIndex, T value) {  Distance parent = (holeIndex - 1) / 2;  //找到父節點  // 當尚未到達頂端，且父節點小於新值(於是不符合 heap 的次序特性)  while (holeIndex > topIndex && *(first + parent) < value) {    *(first + holeIndex) = *(first + parent); //令洞值為父值    holeIndex = parent; //調整洞號，向上提升至父節點    parent = (holeIndex - 1) / 2; //新洞的父節點   }      *(first + holeIndex) = value; //令洞值為新值，完成插入操作}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)));}/*調用此函數時，新元素應已置於底部容器的最尾端 --> 什麼時候置的？ --> stl_heap 不對外開放，只在 STL 內部使用，使用 push_heap 的其他 STL 程式應該注意在調用push_heap 函數前，將新元素置於 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 裡很多這種函數體裡直接調用另一個函數的函數，感覺這樣不太好，增加了堆棧的開銷，//為什麼不直接就調用裡面那個函數呢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 操作的結果應該底部容器的第一個元素  __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; //洞節點的右子節點  while (secondChild < len) { //當還有左、右子節點的時候    if (comp(*(first + secondChild), *(first + (secondChild - 1))))      secondChild--;    *(first + holeIndex) = *(first + secondChild); //令較大值為洞值    holeIndex = secondChild; //令洞號下移至較大子節點處    secondChild = 2 * (secondChild + 1); //找出新洞節點的子節點  }  if (secondChild == len) { //當只有左節點的時候    *(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*) {  //將首值(即要 pop 出來的值)存放在 result 所指處。    *result = *first;  //重新調整 heap ， 洞號為0，欲調整值為 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;  //找出第一個需要重排的子樹的頭部，以 parent 標示出。  Distance parent = (len - 2)/2;      while (true) {    __adjust_heap(first, parent, len, T(*(first + parent)), comp);    if (parent == 0) return; //走完根節點，就結束了。    parent--; //實際上就是沿著第一個父節點從左至右調整值使父節點的值大於(或小於)兩個子節點  }}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) {  //每次執行一次 pop_heap() ，極值被放在尾端  //扣除尾端再執行一次 pop_heap()，次極值又被放在新尾端  //一直這樣下去，最後即可得到排序結果  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: