二叉尋找樹 – C語言實現（摘自資料結構與演算法分析 C語言描述）

一、概述        二叉樹的一個重要的應用是它們在尋找中的使用。使二叉樹成為尋找樹的性質是，對於樹中的每個結點 X，它的左子樹中所有關鍵字值小於X的關索引值，而它的右子樹中所有關鍵字大於X的關索引值。在圖1中，左邊的樹是二叉尋找樹，但右邊的樹則不是（想一想為什麼）。圖1 兩棵二叉樹（只有左邊的樹是尋找樹）二、實現
        因為二叉樹最多有兩個兒子，所以我們可以用指標直接指向它們。樹節點的聲明在結構上類似於雙鏈表的聲明，在聲明中，一個節點就是由Key（關鍵字）資訊加上兩個指向其他節點的指標（Left和Right）組成的結構。檔案名稱：tree.h

#ifndef _Tree_Htypedef 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 */

檔案名稱：tree.c

#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;}PositionFind( ElementType X, SearchTree T ){if ( T == NULL )return NULL;if ( X < T->Element )return Find( X, T->Left );elseif ( X > T->Element )return Find( X, T->Right );else return T;}/* 對二叉尋找樹的FindMin的遞迴實現 */PositionFindMin( SearchTree T ){if ( T == NULL )return NULL;elseif ( T->Left  == NULL )return T;elsereturn FindMin( T->Left );}/* 對二叉尋找樹的FindMax的非遞迴實現 */PositionFindMax( SearchTree T ){if ( T != NULL )while( T->Right != NULL )T = T->Right;return T;}SearchTreeInsert( 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;}}elseif ( X < T->Element )T->Left = Insert( X, T->Left );elseif ( 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!!! */}SearchTreeDelete( ElementType X, SearchTree T ){Position TmpCell;if ( T == NULL)Error( "Element not found" );elseif ( X < T->Element ) /* Go left */T->Left = Delete( X, T->Left );elseif ( 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 );}}

檔案名稱：main.c

#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;}

附錄：上述代碼中用到了Error、FatalError等函數，其實現如下（即fatal.h檔案）：

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

備忘：本文摘自《資料結構與演算法分析 C語言描述 Mark Allen Weiss著》，代碼經gcc編譯測試通過。

附件下載：http://download.csdn.net/detail/shuxiao9058/4212427#tree_20120401.tar.gz