《資料結構》04-樹7 二叉搜尋樹的操作集
阿新 • • 發佈：2018-12-19
題目
本題要求實現給定二叉搜尋樹的5種常用操作。
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; - 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 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
分析
#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;
}
// 插入
BinTree Insert( BinTree BST, ElementType X ){
if(!BST){ // 如果為空，建立新結點
BST = (BinTree)malloc(sizeof(struct TNode));
BST->Data = X;
BST->Left = NULL;
BST->Right = NULL;
}else{
if(X < BST->Data)
BST->Left = Insert(BST->Left,X);
else if(BST->Data < X)
BST->Right = Insert(BST->Right,X);
}
return BST;
}
// 刪除
BinTree Delete( BinTree BST, ElementType X ){
BinTree tmp;
if(!BST){
printf("Not Found\n");
return BST;
}else{
if(X < BST->Data)
BST->Left = Delete(BST->Left,X);
else if(BST->Data < X)
BST->Right = Delete(BST->Right,X);
else{ // 找到要刪除結點
if(BST->Left && BST->Right){ // 如果該結點有左右兒子
tmp = FindMin(BST->Right);
BST->Data = tmp->Data;
BST->Right = Delete(BST->Right,tmp->Data);
}else{
tmp = BST;
if(BST->Left && !BST->Right)
BST = BST->Left;
else if(!BST->Left && BST->Right)
BST = BST->Right;
else
BST = NULL;
free(tmp);
}
}
}
return BST;
}
// 尋找值最小結點
Position FindMin( BinTree BST ){
if(BST)
while(BST->Left)
BST = BST->Left;
return BST;
}
// 尋找值最大結點
Position FindMax( BinTree BST ){
if(BST)
while(BST->Right)
BST = BST->Right;
return BST;
}
// 查詢
Position Find( BinTree BST, ElementType X ){
if(!BST){
return NULL;
}else if(X < BST->Data)
return Find(BST->Left,X);
else if(BST->Data < X)
return Find(BST->Right,X);
else
return BST;
}
// 先序遍歷
void PreorderTraversal( BinTree BT ){
if(BT){
printf(" %d",BT->Data);
PreorderTraversal(BT->Left);
PreorderTraversal(BT->Right);
}
}
// 中序遍歷
void InorderTraversal( BinTree BT ){
if(BT){
InorderTraversal(BT->Left);
printf(" %d",BT->Data);
InorderTraversal(BT->Right);
}
}