AVL树自平衡的几种旋转

标注: AVL树的基本题，仔细想想动手画画RS, LS,LRS,RLS！！code

04-树5 Root of AVL Tree   (25分)

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer $N$ ($\le 20$) which is the total number of keys to be inserted. Then $N$ distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

#include #include #include #define MAX(a,b) (a>b)?a:btypedef int Element;typedef struct AVLtreeNode* AVLTree;struct AVLtreeNode{    Element data;    AVLTree left;    AVLTree right;    int height;};AVLTree AVl_Insertion(Element x,AVLTree T);Element GetHeight(AVLTree A);AVLTree SingleLeftRotation(AVLTree A);AVLTree SingleRightRotation(AVLTree A);AVLTree DoubleLeftRightRotation(AVLTree A);AVLTree DoubleRightLeftRotation(AVLTree A);int main(){   // freopen("11.txt","r",stdin);    int N;    AVLTree T = NULL;    scanf("%d",&N);    while (N--)    {        int x;        scanf("%d",&x);        T = AVl_Insertion(x,T);    }    printf("%d\n",T->data);    return 0;}Element GetHeight(AVLTree A){    int HL,HR,Maxh;    if (A)    {        HL = GetHeight(A->left);        HR = GetHeight(A->right);        Maxh = MAX(HL,HR);        return (Maxh+1);    }    else return 0;}AVLTree AVl_Insertion(Element x,AVLTree T){    if(!T)    {        T = (AVLTree)malloc(sizeof(struct AVLtreeNode));        T->data=x;        T->height = 0;        T->left=T->right=NULL;    }    else if (x < T->data)    {        T->left = AVl_Insertion(x,T->left);        if(GetHeight(T->left)-GetHeight(T->right)==2)        {            if (x < T->left->data)            {                T = SingleLeftRotation(T);            }            else            {                T = DoubleLeftRightRotation(T);            }        }    }    else if (x > T->data)    {        T->right = AVl_Insertion(x,T->right);        if(GetHeight(T->left)-GetHeight(T->right)==-2)        {            if (x > T->right->data)            {                T = SingleRightRotation(T);            }            else            {                T = DoubleRightLeftRotation(T);            }        }    }    T->height = MAX(GetHeight(T->left),GetHeight(T->right))+1;    return T;}AVLTree SingleLeftRotation(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),GetHeight(B->right)) + 1;    return B;}AVLTree SingleRightRotation(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->left),GetHeight(B->right)) + 1;    return B;}AVLTree DoubleLeftRightRotation(AVLTree A){    A->left = SingleRightRotation(A->left);    return SingleLeftRotation(A);}AVLTree DoubleRightLeftRotation(AVLTree A){    A->right = SingleLeftRotation(A->right);    return SingleRightRotation(A);}