04-樹7 二叉搜尋樹的操作集 (30分)
阿新 • • 發佈:2020-08-02
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;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
提交測試程式碼:
BinTree Insert(BinTree BST, ElementType X) { if (!BST) { BST = (BinTree)malloc(sizeof(struct TNode)); BST->Data = X; BST->Left = NULL; 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) { printf("Not Found\n"); } else if (BST->Data > X) { BST->Left = Delete(BST->Left, X); } else if (BST->Data < X) { BST->Right = Delete(BST->Right, X); } else if (BST->Left != NULL && BST->Right == NULL) { BinTree tmp = BST; BST = BST->Left; free(tmp); } else if (BST->Left == NULL && BST->Right != NULL) { BinTree tmp = BST; BST = BST->Right; free(tmp); } else if (BST->Left == NULL && BST->Right == NULL) { free(BST); BST = NULL; } else { Position tmp = FindMin(BST->Right); BST->Data = tmp->Data; BST->Right = Delete(BST->Right, BST->Data); } return BST; } Position Find(BinTree BST, ElementType X) { if (!BST) { return NULL; } else if (BST->Data > X) { return Find(BST->Left, X); } else if (BST->Data < X) { return Find(BST->Right, X); } else { return BST; } } Position FindMin(BinTree BST) { if (!BST) { return NULL; } else if (BST->Left != NULL) { return FindMin(BST->Left); } else { return BST; } } Position FindMax(BinTree BST) { if (!BST) { return NULL; } else if (BST->Right != NULL) { return FindMax(BST->Right); } else { return BST; } }
提測結果:
完整自測程式碼:
#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; } void PreorderTraversal(BinTree T){ if (!T) { return; } printf(" %d", T->Data); if(T->Left){ PreorderTraversal(T->Left); } if (T->Right){ PreorderTraversal(T->Right); } } void InorderTraversal(BinTree T) { if (!T) { return; } if (T->Left) { InorderTraversal(T->Left); } printf(" %d", T->Data); if (T->Right) { InorderTraversal(T->Right); } } BinTree Insert(BinTree BST, ElementType X) { if (!BST) { BST = (BinTree)malloc(sizeof(struct TNode)); BST->Data = X; BST->Left = NULL; 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) { printf("Not Found\n"); } else if (BST->Data > X) { BST->Left = Delete(BST->Left, X); } else if (BST->Data < X) { BST->Right = Delete(BST->Right, X); } else if (BST->Left != NULL && BST->Right == NULL) { BinTree tmp = BST; BST = BST->Left; free(tmp); } else if (BST->Left == NULL && BST->Right != NULL) { BinTree tmp = BST; BST = BST->Right; free(tmp); } else if (BST->Left == NULL && BST->Right == NULL) { free(BST); BST = NULL; } else { Position tmp = FindMin(BST->Right); BST->Data = tmp->Data; BST->Right = Delete(BST->Right, BST->Data); } return BST; } Position Find(BinTree BST, ElementType X) { if (!BST) { return NULL; } else if (BST->Data > X) { return Find(BST->Left, X); } else if (BST->Data < X) { return Find(BST->Right, X); } else { return BST; } } Position FindMin(BinTree BST) { if (!BST) { return NULL; } else if (BST->Left != NULL) { return FindMin(BST->Left); } else { return BST; } } Position FindMax(BinTree BST) { if (!BST) { return NULL; } else if (BST->Right != NULL) { return FindMax(BST->Right); } else { return BST; } }