AVL Insertion(30分)

AVL Insertion(30分)

You are supposed to implement the Insert function, which inserts an integer Key into an AVL tree T. The resulting tree must be returned.

Format of function:

AVLTree Insert ( AVLTree T, int Key );

where AVLTree is defined as the following:

typedef struct AVLNode *PtrToAVLNode;
struct AVLNode{
    int Key;
    PtrToAVLNode Left;
    PtrToAVLNode Right;
    int Height;
};
typedef PtrToAVLNode AVLTree;

Sample program of judge:

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

typedef struct AVLNode *PtrToAVLNode;
struct AVLNode{
    int Key;
    PtrToAVLNode Left;
    PtrToAVLNode Right;
    int Height;
};
typedef PtrToAVLNode AVLTree;

AVLTree Insert ( AVLTree T, int Key );
void PostOrderPrint( AVLTree T ); /* details omitted */
void InOrderPrint( AVLTree T );   /* details omitted */

int main()
{
    int N, Key, i;
    AVLTree T = NULL;

    scanf("%d", &N);
    for ( i=0; i<N; i++ ) {
        scanf("%d", &Key);
        T = Insert( T, Key );
    }
    PostOrderPrint( T );
    InOrderPrint( T );

    return 0;
}
/* Your function will be put here */

Sample Input:

7
88 70 61 96 120 90 65

Sample Output:

Post-order: 61 70 65 90 120 96 88
In-order: 61 65 70 88 90 96 120

---

代码:

我也不知道为什么只给了一个函数,在答题框里能写这么多函数,但是好像就是可以

得最大值 ,求树高 ,左单旋 ,右单旋 ,左右双旋 ,右左双旋

这先写了六个预备函数,然后再写的插入函数

int Max(int a, int b){
    return a>b?a:b;
}
 
int GetHeight(AVLTree A){
    if(A==NULL)
        return 0;
    return A->Height;
}
 
AVLTree SingleLeftRotation(AVLTree A){
    AVLTree B=A->Right;
    A->Right=B->Left;
    B->Left=A;
    A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
    B->Height = Max(GetHeight(B->Right), A->Height) + 1;
    return B;
}
 
AVLTree SingleRightRotation(AVLTree A){
    AVLTree B=A->Left;
    A->Left=B->Right;
    B->Right=A;
    A->Height=Max(GetHeight(A->Left), GetHeight(A->Right))+1;
    B->Height=Max(GetHeight(B->Left),A->Height)+1;
    return B;
}
 
AVLTree DoubleLeftRightRotation(AVLTree A){
    A->Right = SingleRightRotation(A->Right);
    return SingleLeftRotation(A);
}
 
 
AVLTree DoubleRightLeftRotation(AVLTree A){
    A->Left = SingleLeftRotation(A->Left);
    return SingleRightRotation(A);
}
 
 
AVLTree Insert(AVLTree T,int X){
    if(!T){
        T=(AVLTree)malloc(sizeof(struct AVLNode));
        T->Key=X;
        T->Height=1;
        T->Left=T->Right=NULL;
    }
 
    else if(X<T->Key){ //插入左子树
        T->Left=Insert(T->Left, X);
        if(GetHeight(T->Left)-GetHeight(T->Right)==2){
            if (X<T->Left->Key) {
                T=SingleRightRotation(T);
            }
            else
                T=DoubleRightLeftRotation(T);
        }
    }
 
    else if(X>T->Key){
        T->Right=Insert(T->Right, X);
        if(GetHeight(T->Left)-GetHeight(T->Right)==-2){
            if (X>T->Right->Key)
                T=SingleLeftRotation(T);
            else
                T=DoubleLeftRightRotation(T);
 
        }
    }
    T->Height=Max(GetHeight(T->Left), GetHeight(T->Right))+1;
    return T;
}