左式堆中每一个节点left child的零路径长至少与right child的零路径长一样。任一节点的零路径长为从该节点到一个不具有两个儿子的节点的最短路径的长。下图为一棵左式树。
对左式堆的基本操作是合并，为了合并两个堆，递归的做法是先比较它们的根，递归地将具有较大根值的堆与具有较小根值的堆的右子堆合并。
#ifndef LEFTIST_HEAP_H
#define LEFTIST_HEAP_H
#include "dsexceptions.h"
#include <iostream>
using namespace std;
template <typename Comparable>
class LeftistHeap
{
public:
LeftistHeap() : root{
nullptr } {
}
LeftistHeap(const LeftistHeap & rhs) : root{
nullptr }
{
root = clone(rhs.root);
}
LeftistHeap(LeftistHeap && rhs) : root{
rhs.root }
{
rhs.root = nullptr;
}
~LeftistHeap()
{
makeEmpty();
}
LeftistHeap & operator=(const LeftistHeap & rhs)
{
LeftistHeap copy = rhs;
std::swap(*this, copy);
return *this;
}
LeftistHeap & operator=(LeftistHeap && rhs)
{
std::swap(root, rhs.root);
return *this;
}
bool isEmpty() const
{
return root == nullptr;
}
const Comparable & findMin() const
{
if (isEmpty())
throw UnderflowException{
};
return root->element;
}
void insert(const Comparable & x)
{
root = merge(new LeftistNode{
x}, root);
}
void insert(Comparable && x)
{
root = merge(new LeftistNode{
std::move(x)}, root);
}
void deleteMin()
{
if (isEmpty())
throw UnderflowException{
};
LeftistNode *oldRoot = root;
root = merge(root->left, root->right);
delete oldRoot;
}
void deleteMin(Comparable & minItem)
{
minItem = findMin();
deleteMin();
}
void makeEmpty()
{
reclaimMemory(root);
root = nullptr;
}
void merge(LeftistHeap & rhs)
{
if (this == &rhs)
return;
root = merge(root, rhs.root);
rhs.root = nullptr;
}
private:
struct LeftistNode
{
Comparable element;
LeftistNode *left;
LeftistNode *right;
int npl;
LeftistNode(const Comparable & e, LeftistNode *lt = nullptr,
LeftistNode *rt = nullptr, int np = 0)
: element{
e}, left{
lt}, right{
rt}, npl{
np} {
}
LeftistNode(Comparable && e, LeftistNode *lt = nullptr,
LeftistNode *rt = nullptr, int np = 0)
: element{
std::move(e)}, left{
lt}, right{
rt}, npl{
np} {
}
};
LeftistNode *root;
LeftistNode *merge(LeftistNode *h1, LeftistNode *h2)
{
if (h1 == nullptr)
return h2;
if (h2 == nullptr)
return h1;
if (h1->element < h2->element)
return merge1(h1, h2);
else
return merge1(h2, h1);
}
LeftistNode *merge1(LeftistNode *h1, LeftistNode *h2)
{
if (h1->left == nullptr)
h1->left = h2;
else {
h1->right = merge(h1->right, h2);
if (h1->left->npl < h1->right->npl)
swapChildren(h1);
h1->npl = h1->right->npl + 1;
}
return h1;
}
void swapChildren(LeftistNode *t)
{
LeftistNode *tmp = t->left;
t->left = t->right;
t->right = tmp;
}
void reclaimMemory(LeftistNode *t)
{
if (t != nullptr) {
reclaimMemory(t->left);
reclaimMemory(t->right);
delete t;
}
}
LeftistNode *clone(LeftistNode *t) const
{
if (t == nullptr)
return nullptr;
else
return new LeftistNode{
t->element, clone(t->left), clone(t->right), t->npl};
}
};
#endif