template <class T>
class LeftistNode{public:T key;                // 关键字(键值)int npl;            // 零路经长度(Null Path Length)LeftistNode *left;    // 左孩子LeftistNode *right;    // 右孩子
LeftistNode(T value, LeftistNode *l, LeftistNode *r):key(value), npl(0), left(l),right(r) {}
};

template <class T>
class LeftistHeap {private:LeftistNode<T> *mRoot;    // 根结点public:LeftistHeap();~LeftistHeap();// 前序遍历"左倾堆"void preOrder();// 中序遍历"左倾堆"void inOrder();// 后序遍历"左倾堆"void postOrder();// 将other的左倾堆合并到this中。void merge(LeftistHeap<T>* other);// 将结点(key为节点键值)插入到左倾堆中void insert(T key);// 删除结点(key为节点键值)void remove();// 销毁左倾堆void destroy();// 打印左倾堆void print();private:// 前序遍历"左倾堆"void preOrder(LeftistNode<T>* heap) const;// 中序遍历"左倾堆"void inOrder(LeftistNode<T>* heap) const;// 后序遍历"左倾堆"void postOrder(LeftistNode<T>* heap) const;// 交换节点x和节点yvoid swapNode(LeftistNode<T> *&x, LeftistNode<T> *&y);// 合并"左倾堆x"和"左倾堆y"LeftistNode<T>* merge(LeftistNode<T>* &x, LeftistNode<T>* &y);// 将结点(z)插入到左倾堆(heap)中LeftistNode<T>* insert(LeftistNode<T>* &heap, T key);// 删除左倾堆(heap)中的结点(z)，并返回被删除的结点LeftistNode<T>* remove(LeftistNode<T>* &heap);// 销毁左倾堆void destroy(LeftistNode<T>* &heap);// 打印左倾堆void print(LeftistNode<T>* heap, T key, int direction);
};

/** 合并"左倾堆x"和"左倾堆y"*/
template <class T>
LeftistNode<T>* LeftistHeap<T>::merge(LeftistNode<T>* &x, LeftistNode<T>* &y)
{if(x == NULL)return y;if(y == NULL)return x;// 合并x和y时，将x作为合并后的树的根；// 这里的操作是保证: x的key < y的keyif(x->key > y->key)swapNode(x, y);// 将x的右孩子和y合并，"合并后的树的根"是x的右孩子。x->right = merge(x->right, y);// 如果"x的左孩子为空" 或者 "x的左孩子的npl<右孩子的npl"// 则，交换x和yif(x->left == NULL || x->left->npl < x->right->npl){LeftistNode<T> *tmp = x->left;x->left = x->right;x->right = tmp;}// 设置合并后的新树(x)的nplif (x->right == NULL || x->left == NULL)x->npl = 0;elsex->npl = (x->left->npl > x->right->npl) ? (x->right->npl + 1) : (x->left->npl + 1);return x;
}/** 将other的左倾堆合并到this中。*/
template <class T>
void LeftistHeap<T>::merge(LeftistHeap<T>* other)
{mRoot = merge(mRoot, other->mRoot);
}

/* * 将结点插入到左倾堆中，并返回根节点** 参数说明：*     heap 左倾堆的根结点*     key 插入的结点的键值* 返回值：*     根节点*/
template <class T>
LeftistNode<T>* LeftistHeap<T>::insert(LeftistNode<T>* &heap, T key)
{LeftistNode<T> *node;    // 新建结点// 新建节点node = new LeftistNode<T>(key, NULL, NULL);if (node==NULL){cout << "ERROR: create node failed!" << endl;return heap;}return merge(mRoot, node);
}template <class T>
void LeftistHeap<T>::insert(T key)
{mRoot = insert(mRoot, key);
}

/* * 删除结点，返回根节点** 参数说明：*     heap 左倾堆的根结点* 返回值：*     根节点*/
template <class T>
LeftistNode<T>* LeftistHeap<T>::remove(LeftistNode<T>* &heap)
{if (heap == NULL)return NULL;LeftistNode<T> *l = heap->left;LeftistNode<T> *r = heap->right;// 删除根节点delete heap;return merge(l, r); // 返回左右子树合并后的新树
}template <class T>
void LeftistHeap<T>::remove()
{mRoot = remove(mRoot);
}