二叉查找树 - C语言实现（摘自数据结构与算法分析 C语言描述）

来源：互联网发布：淘宝美图软件编辑：程序博客网时间：2024/05/01 07:17

一、概述

二叉树的一个重要的应用是它们在查找中的使用。使二叉树成为查找树的性质是，对于树中的每个结点X，它的左子树中所有关键字值小于X的关键值，而它的右子树中所有关键字大于X的关键值。在图1中，左边的树是二叉查找树，但右边的树则不是（想一想为什么）。

图1 两棵二叉树（只有左边的树是查找树）

二、实现

因为二叉树最多有两个儿子，所以我们可以用指针直接指向它们。树节点的声明在结构上类似于双链表的声明，在声明中，一个节点就是由Key（关键字）信息加上两个指向其他节点的指针（Left和Right）组成的结构。

文件名：tree.h

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#ifndef _Tree_H
typedef int ElementType;
struct TreeNode;
typedef struct TreeNode *Position;
typedef struct TreeNode *SearchTree;
SearchTree MakeEmpty( SearchTree T );
Position Find( ElementType X, SearchTree T );
Position FindMin( SearchTree T );
Position FindMax( SearchTree T );
SearchTree Insert( ElementType X, SearchTree T );
SearchTree Delete( ElementType X, SearchTree T );
ElementType Retrieve( Position P );
void PrintElement( SearchTree T );
void PreOrder( SearchTree T );
void InOrder( SearchTree T );
void PostOrder( SearchTree T );
#endif /* Tree_H */

文件名：tree.c

[cpp] view plaincopyprint?

#include "fatal.h"
#include "tree.h"
struct TreeNode
{
ElementType Element;
SearchTree Left;
SearchTree Right;
};
SearchTree
MakeEmpty( SearchTree T )
{
if ( T != NULL )
{
MakeEmpty( T->Left );
MakeEmpty( T->Right );
free( T );
}
return NULL;
}
Position
Find( ElementType 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;
}
/* 对二叉查找树的FindMin的递归实现 */
Position
FindMin( SearchTree T )
{
if ( T == NULL )
return NULL;
else
if ( T->Left == NULL )
return T;
else
return FindMin( T->Left );
}
/* 对二叉查找树的FindMax的非递归实现 */
Position
FindMax( SearchTree T )
{
if ( T != NULL )
while( T->Right != NULL )
T = T->Right;
return T;
}
SearchTree
Insert( ElementType X, SearchTree T )
{
if ( T == NULL )
{
/* Create and return a one-node tree */
T = malloc( sizeof( struct TreeNode ) );
if ( T== NULL )
FatalError( "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 );
/* Else X is in the tree already;we'll do nothing */
return T; /* Do not forget this line!!! */
}
SearchTree
Delete( ElementType X, SearchTree T )
{
Position TmpCell;
if ( T == NULL)
Error( "Element not found" );
else
if ( X < T->Element ) /* Go left */
T->Left = Delete( X, T->Left );
else
if ( X > T->Element ) /* Go Right */
T->Right = Delete( X, T->Left );
else /* Found element to be deleted */
if ( T->Left && T->Right ) /*Two children */
{
/* Replace with smallest in right subtree */
TmpCell = FindMin( T->Right );
T->Element = TmpCell->Element;
T->Right = Delete( T->Element, T->Right );
}
else /* One or zero children */
{
TmpCell = T;
if ( T->Left == NULL) /* Also handles 0 children */
T = T->Right;
else if ( T->Right == NULL )
T = T->Left;
free( TmpCell );
}
return T;
}
ElementType
Retrieve( Position P )
{
return P->Element;
}
void
PrintElement( SearchTree T )
{
printf( "%3d ", Retrieve( T ) );
}
void
PreOrder( SearchTree T )
{
if (T != NULL )
{
PrintElement( T );
PreOrder( T->Left );
PreOrder( T->Right );
}
}
void
InOrder( SearchTree T )
{
if (T != NULL )
{
InOrder( T->Left );
PrintElement( T );
InOrder( T->Right );
}
}
void
PostOrder( SearchTree T )
{
if ( T != NULL )
{
PostOrder( T->Left );
PostOrder( T->Right );
PrintElement( T );
}
}

文件名：main.c

[cpp] view plaincopyprint?

#include "tree.h"
#include <stdio.h>
int main()
{
SearchTree T = NULL;
int i, j, m, n;
ElementType tmp;
printf( "Number of Elements:" );
scanf( "%d", &n );
for ( i = 0; i < n; i++)
{
scanf( "%d", &tmp );
T = Insert( tmp, T );
}
printf( "\nPreOrder :" );
PreOrder( T );
printf( "\nInOrder :" );
InOrder( T );
printf( "\nPostOrder:" );
PostOrder( T );
printf( "\n" );
return 0;
}

附录：上述代码中用到了Error、FatalError等函数，其实现如下（即fatal.h文件）：

[cpp] view plaincopyprint?

#include <stdio.h>
#include <stdlib.h>
#define Error( Str ) FatalError( Str )
#define FatalError( Str ) fprintf( stderr, "%s\n", Str ), exit( 1 )

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