零路徑長度(null path length, NPL),NPL(X)定義爲從X到一個沒有兩個兒子的節點的最短路徑的長。因此具有0個或1個兒子的節點的NPL爲0,而NPL(NULL) = -1。
左式堆性質是:對於隊中的每一個節點X,左兒子的零路徑長至少與右兒子的零路徑長一樣大。左式堆與二叉堆具有相同的堆序性質,惟一的區別在於左式堆不是理想平衡的,而實際上是趨於非常不平衡的。左式堆的基本操作是合併。其中,插入只是合併的特殊情形,因爲我們可以把插入看成是單個節點堆與一個大的堆的Merge。注意,最小的元素在根節點。
如下圖左式堆合併
fatal.h錯誤處理
#include <stdio.h>
#include <stdlib.h>
#define Error(str) FatalError(str)
#define FatalError(str) fprintf(stderr, "%s\n", str),exit(1)
leftheap.h左式堆函數聲明
typedef int ElementType;
#ifndef LEFTHEAP_H
#define LEFTHEAP_H
struct TreeNode
{
ElementType Element;
struct TreeNode *Left;
struct TreeNode *Right;
int Npl;//零路徑長
};
typedef struct TreeNode *PriorityQueue;
PriorityQueue Initialize(void);//初始化堆
ElementType FindMin(PriorityQueue H);//查找最小值
int IsEmpty(PriorityQueue H);//判斷是否爲空
PriorityQueue Merge(PriorityQueue H1, PriorityQueue H2);//合併兩個左式堆
PriorityQueue Insert(ElementType X, PriorityQueue H);//插入節點,即單節點與堆合併
PriorityQueue DeleteMin(PriorityQueue H);//刪除最小值
#endif
leftheap.c左式堆具體實現
#include "fatal.h"
#include "leftheap.h"
#include <stdlib.h>
PriorityQueue Initialize(void)
{
return NULL;
}
static PriorityQueue Merge1(PriorityQueue H1, PriorityQueue H2);
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);
}
void SwapChildren(PriorityQueue H)
{
PriorityQueue Tmp;
Tmp = H->Left;
H->Left = H->Right;
H->Right = Tmp;
}
static PriorityQueue Merge1(PriorityQueue H1, PriorityQueue H2)
{
if(H1->Left == NULL)
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;
}
PriorityQueue Insert(ElementType X, PriorityQueue H)
{
PriorityQueue SingleNode;
SingleNode = (PriorityQueue)malloc(sizeof(struct TreeNode));
if(SingleNode == NULL)
FatalError("Out of space");
else
{
SingleNode->Element = X;
SingleNode->Npl = 0;
H = Merge(SingleNode, H);
}
return H;
}
PriorityQueue DeleteMin(PriorityQueue H)
{
PriorityQueue LeftHeap, RightHeap;
if(IsEmpty(H))
{
Error("Priority queue is empty");
return H;
}
LeftHeap = H->Left;
RightHeap = H->Right;
free(H);
return Merge(LeftHeap, RightHeap);
}
ElementType FindMin(PriorityQueue H)
{
if(!IsEmpty(H))
return H->Element;
Error("Priority queue is empty");
return 0;
}
int IsEmpty(PriorityQueue H)
{
return H == NULL;
}
main.c測試左式堆
#include "leftheap.h"
#include <stdio.h>
#include <stdlib.h>
#define MaxSize 5000
int main()
{
PriorityQueue H;
int i, j;
H = Initialize();
for(i = 0, j = MaxSize / 2; i < MaxSize; i++, j = (j + 17) % MaxSize)
Insert(j, H);
j = 0;
while(!IsEmpty(H))
if(FindMin(H) != j++)
printf("Error in DeleteMin, %d\n", j);
else
H = DeleteMin(H);
printf("Done...\n");
system("Pause");
return 0;
}