二叉查找树特点每个节点X,左子树的值都都小于X,右子树的值都大于X
二叉树声明
#ifndef _Tree_H
struct TreeNode;
typedef struct TreeNode *Position;
typedef struct TreeNode *SearchTree;
SearchTree MakeEmpty(SearchTree T);
Position Find(int X, SearchTree T);
Position FindMin(SearchTree T);
Position FindMax(SearchTree T);
SearchTree Insert(int X, SearchTree T);
SearchTree Delete(int X, SearchTree T);
int Retrieve(Position P);
#endif
二叉树实现
/* 二叉查找树声明 */
struct TreeNode
{
int Element;
SearchTree Left;
SearchTree Right;
};
/* 建立一棵空树 */
SearchTree MakeEmpty(SearchTree T)
{
if(T != NULL)
{
MakeEmpty(T->Left);
MakeEmpty(T->Right);
free(T);
}
return NULL;
}
/* 查找某个节点 */
Position Find(int X, SearchTree T)
{
if(T == NULL)
return NULL;
if(X < T->Element)
return Find(X, T->Left);
else if(X > T->Element)
return Find(X, T->Right);
else
return T;
}
/* 查找二叉树最小节点 递归实现 */
Position FindMin(SearchTree T)
{
if(T == NULL)
return NULL;
else if(T->Left == NULL)
return T;
else
return FindMin(T->Left);
}
/* 查找二叉树最大节点 非递归实现 */
Position FindMax(SearchTree T)
{
if(T != NULL)
while(T->Right != NULL)
T = T->Right;
return T;
}
/* 插入元素到二叉树 */
SearchTree Insert(int X, SearchTree T)
{
if(T == NULL)
{
/* 创建并返回一个节点的树 */
T = malloc(sizeof(struct TreeNode));
if(T == NULL)
fprintf(stderr, "Out of space!!!");
else
{
T->Element = X;
T->Left = T->Right = NULL;
}
}
else if(X < T->Element)
T->Left = Insert(X, T->Left);
else if(X > T->Element)
T->Right = Insert(X, T->Right);
/* 如果X已经在树中就啥也不做 */
return T;
}
/* 删除节点 */
SearchTree Delete(int X, SearchTree T)
{
Position TmpCell;
if(T == NULL)
fprintf(stderr, "Element not found!!!");
else if(X < T->Element) // go to left
T->Left = Delete(X, T->Left);
else if(X > T->Element) // go to right
T->Right = Delete(X, T->Right);
else /* 找到删除的元素 */
if(T->Left && T->Right) // 有2个子节点
{
/* 替换右子树中最小的节点 */
TmpCell = FindMin(T->Right);
T->Element = TmpCell->Element;
T->Right = Delete(T->Element, T->Right);
}
else //有一个或没有子节点
{
TmpCell = T;
if(T->Left == NULL)
T = T->Right;
else if(T->Right == NULL)
T= T->Left;
free(TmpCell);
}
return T;
}
/* 取某个节点的值 */
int Retrieve(Position P)
{
return P->Element;
}
二叉树测试
#include <stdio.h>
#include <stdlib.h>
#include "Tree.h"
int main(void)
{
SearchTree tree = NULL; // 不要忘了初始化
tree = Insert(50, tree);
ShowTree(tree);
printf("\n");
Insert(42, tree);
ShowTree(tree);
printf("\n");
Insert(36, tree);
Insert(48, tree);
Insert(77, tree);
Insert(3, tree);
Insert(28, tree);
Insert(98, tree);
Insert(76, tree);
Insert(1, tree);
ShowTree(tree);
printf("\n");
Position p = Find(77, tree);
if(p != NULL)
printf("find %d ", Retrieve(p));
else
printf("not found 77");
Delete(48, tree);
ShowTree(tree);
printf("\n");
return 0;
}