04-树7 二叉搜索树的操作集

　　二叉搜索树的基本操作。

　　其中Delete操作时有多种情况，需要严谨考虑。

#include <stdio.h>
#include <stdlib.h>

typedef int ElementType;
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */
void InorderTraversal( BinTree BT );  /* 中序遍历，由裁判实现，细节不表 */

BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );

int main()
{
    BinTree BST, MinP, MaxP, Tmp;
    ElementType X;
    int N, i;

    BST = NULL;
    scanf("%d", &N);
    for ( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Insert(BST, X);
    }
    printf("Preorder:"); PreorderTraversal(BST); printf("\n");
    MinP = FindMin(BST);
    MaxP = FindMax(BST);
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        Tmp = Find(BST, X);
        if (Tmp == NULL) printf("%d is not found\n", X);
        else {
            printf("%d is found\n", Tmp->Data);
            if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);
            if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);
        }
    }
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Delete(BST, X);
    }
    printf("Inorder:"); InorderTraversal(BST); printf("\n");

    return 0;
}

BinTree Insert( BinTree BST, ElementType X )
{
    if(!BST){
        BST = (BinTree)malloc(sizeof(struct TNode));
        BST->Data = X;
        BST->Left = NULL;
        BST->Right = NULL;        
    }
    if(X > BST->Data)
        BST->Right = Insert(BST->Right, X);
    if(X < BST->Data)
        BST->Left = Insert(BST->Left, X);
    return BST;
}

BinTree Delete( BinTree BST, ElementType X )
{
    Position Tmp;
    if(!BST)
        printf("Not Found\n");
    else if(X < BST->Data)
        BST->Left = Delete(BST->Left, X);
    else if(X > BST->Data)
        BST->Right = Delete(BST->Right, X);
    else{  //找到了要删除的结点
        if(BST->Left && BST->Right){  //要删除的结点有左右子树
            Tmp = FindMin(BST->Right);
            BST->Data = Tmp->Data;
            BST->Right = Delete(BST->Right, BST->Data);
        }else{
            Tmp = BST;
            if(!BST->Left)
                BST = BST->Right;
            else if(!BST->Right)
                BST = BST->Left;
            free(Tmp);
        }
    }
    return BST;
}

Position Find( BinTree BST, ElementType X )
{
    if(!BST)
        return NULL;
    if(X > BST->Data)
        return Find(BST->Right, X);
    else if(X < BST->Data)
        return Find(BST->Left, X);
    else 
        return BST;
}

Position FindMin( BinTree BST )
{
    if(!BST)
        return NULL;
    else if(!BST->Left)
        return BST;
    else
        return FindMin(BST->Left);
}

Position FindMax( BinTree BST )
{
    if(BST){
        while(BST->Right)
            BST = BST->Right;
    }
    return BST;
}