优先队列之左式堆

像二叉堆那样，左式堆(leftist heap)也具有结构特性和有序性。左式堆也是二叉树。但左式堆不是理想平衡的，趋向于偏左。

零路径长(null path length,NPL)Npl(X)定义为从X到一个没有两个儿子的节点的最短路径长。因此，具有0个或1个儿子的节点的Npl为0，而Npl(NULL)=-1。

任一节点的零路径长比它的诸儿子节点的零路径长的最小值多1.

左式堆的性质：对于堆中的每一个节点X,左儿子的零路径长至少与右儿子的零路径长一样大。
在右路径上有r个节点的左式树必然至少有2r-1 个节点。

#ifndef _LeftHeap_H

struct TreeNode;
typedef struct TreeNode *PriorityQueue;

/*Minimal set of priority queue operations */
/*Note that nodes will be shared among several */
/*leftist heaps after a merge; the user must */
/*make sure to not use the old leftist heaps */

PriorityQueue Initialize(void);
ElementType FindMin(PriorityQueue H);
int IsEmpty(PriorityQueue H);
PriorityQueue Merge(PriorityQueue H1, PriorityQueue H2);

#define Insert(X,H) (H=iNSERT1((x),H))
/*DeleteMin macro is left as an exercise */

PriorityQueue Insert1(ElementType X, PriorityQueue H):
PriorityQueue DeleteMin1(PriorityQueue H);

#endif

/*Place in implementation fiel*/
struct TreeNode
{
ElementType Element;
PriorityQueue Left;
PriorityQueue Right;
int Npl;
};

PriorityQueue Merge(PriorityQueue H1, PriorityQueue H2)
{
if(H1==NULL)
{
return H2;
}
if(H2==NULL)
{
return H1;
}
if(H1->Element < H2->Element )
{
return Merge1(H1,H2);
}
else
{
return Merge1(H2,H1);
}
}

static PriorityQueue Merge1(PriorityQueue H1,PriorityQueue H2)
{
if(H1->Left==NULL)
H1->Left=H2;
else
{
H1->Right=Merge(H->Right,H2);
if(H1->Left->Npl < H1->Right->Npl)
SwapChildren(H1);
H1->Npl=H1->Right->Npl +1;
}
return H1;
}

PriorityQueue Insert1( ElementType X, PriorityQueue H)
{
PriorityQueue SingleNode;
SingleNode=malloc(sizeof(struct TreeNode));
if(SingleNode==NULL)
printf("Out of space!!!");
else
{
SingleNode->Element=X; SingleNode->Npl=0;
SingleNode->Left=SingleNode->Right=NULL;
H=Merge(SingleNode,H);
}
return H;
}

PriorityQueue DeleteMin1(PriorityQueue H)
{
PriorityQueue LeftHeap,RightHeap;
if(IsEmpty(H))
{
printf("Priority queu is empty!");
return H;
}
LeftHeap=H->Left;
RightHeap=H->Right;
free(H);
return Merge(LeftHeap,RightHeap);
}