二叉搜尋樹的操作集

函式介面定義：

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 );

其中BinTree結構定義如下：

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

• 函式Insert將X插入二叉搜尋樹BST並返回結果樹的根結點指標；
• 函式Delete將X從二叉搜尋樹BST中刪除，並返回結果樹的根結點指標；如果X不在樹中，則列印一行Not Found並返回原樹的根結點指標；
• 函式Find在二叉搜尋樹BST中找到X，返回該結點的指標；如果找不到則返回空指標；
• 函式FindMin返回二叉搜尋樹BST中最小元結點的指標；
• 函式FindMax返回二叉搜尋樹BST中最大元結點的指標。

裁判測試程式樣例：

#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 ); /* 先序遍歷，由裁判實現，細節不表 */
void InorderTraversal( BinTree BT );  /* 中序遍歷，由裁判實現，細節不表 */

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;
}
/* 你的程式碼將被嵌在這裡 */

輸入樣例：

10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3

輸出樣例：

Preorder: 5 2 1 0 4 8 6 7 10 9
6 is found
3 is not found
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is found
Not Found
Inorder: 1 2 4 6 8 9

 

BinTree Insert( BinTree BST, ElementType X )
{
  if(BST==NULL){
    BST=(BinTree)malloc(sizeof(BinTree));
    BST->Data=X;
    BST->Left=BST->Right=NULL;
  }
  else 
  {
        if(BST->Data>X)
      {
        BST->Left=Insert(BST->Left,X);
      }
      else if(BST->Data<X) 
      {
        BST->Right=Insert(BST->Right,X);
      }
  }
      return BST;
}
BinTree Delete( BinTree BST, ElementType X ){
	
	if(BST==NULL){
		printf("Not Found\n");
	}
	else{ 
		if(X>BST->Data)
			BST->Right=Delete(BST->Right,X);
		else if(X<BST->Data)
			BST->Left=Delete(BST->Left,X);
		else {
			if(BST->Left&&BST->Right){
				Position tmp=FindMin(BST->Right);
				BST->Data=tmp->Data;
				BST->Right=Delete(BST->Right,BST->Data);
			}
			else{
				Position tmp=BST;
				if(BST->Left)
					BST=BST->Left;
				else
					BST=BST->Right;
				free(tmp);
			}
		}
	}
	return BST;
}
Position Find( BinTree BST, ElementType X )
{
  if(BST)
  {
  if(X==BST->Data)return BST;
  else if(X>BST->Data)return Find(BST->Right,X);
	else return Find(BST->Left,X); 
  }
  return BST;
}
Position FindMin( BinTree BST )
{ if(BST==NULL)return BST;
  if(BST->Left)FindMin(BST->Left);
  else return BST;
}
Position FindMax( BinTree BST )
{ if(BST==NULL)return BST;
  if(BST->Right)FindMax(BST->Right);
  else return BST;
}