平衡二叉树的调整模版

typedef struct avltreenode *avltree;
typedef struct avltreenode{
    int data;
    avltree left;
    avltree right;
    int height;
};

int getheight(avltree a)
{
    if(a==NULL) return -1;
    return a->height;
}

//a必须有一个左子结点b
//a与b做左单旋，更新a与b高度，返回新的根结点b
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),a->height)+1;

    return b;
}

//右单旋
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->right),a->height)+1;

    return b;
}

//左右双旋
//a必须有一个左子结点b，且b必须有一个右子结点c
//a，b，c,做两次单旋，返回新的根结点c
//先对b和c做右单旋，在对a和c做左单旋
avltree doubleleftrightrotation(avltree a)
{
    a->left=singlerightrotation(a->left);

    return singleleftrotation(a);
}

//右左双旋
avltree doublerightleftrotation(avltree a)
{
    a->right=singleleftrotation(a->right);

    return singlerightrotation(a);
}

avltree avl_insertion(int x,avltree t)
{
    /*将X插入avl树T中，并返回调整后的avl树*/
    if(!t)/*插入空树，则新建包含一个结点的树*/
    {
        t=(avltree)malloc(sizeof(struct avltreenode));
        t->data=x;
        t->height=0;
        t->left=t->right=NULL;
    }/*插入空树结束*/
    else if(x<t->data)
    {
        t->left=avl_insertion(x,t->left);
        if(getheight(t->left)-getheight(t->right)==2)
        {
            /*需要左旋*/
            if(x<t->left->data)
                t=singleleftrotation(t);//左单旋 singleleftrotation
            else
                t=doubleleftrightrotation(t);//左右双旋
        }
    }
    else if(x>t->data)
    {
        t->right=avl_insertion(x,t->right);
        if(getheight(t->left)-getheight(t->right)==-2)
        {
            /*需要右旋*/
            if(x>t->right->data)
                t=singlerightrotation(t);//右单旋
            else
                t=doublerightleftrotation(t);//右左双旋
        }
    }

    //x=data，无须插入
    t->height=max(getheight(t->left),getheight(t->right))+1;
    return t;
}