AVL--平衡二叉查找树

平衡二叉树失衡的四种情况：

AVL树节点声明：

struct AvlNode;
typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

struct AvlNode
{
    ElementType Element;
    AvlTree Left;
    AvlTree Right;
    int Height;
};

static int Height(Position P)
{
    if (P == NULL)
        return -1;
    else
        return P->Height;
} 

对于第一种情况（左左）---（右右类似）：

执行的变换代码为：

/* 左左情况下 */
static Position SingleRotateWithLeft(Position K2)
{
    Position K1;

    K1 = K2->Left;
    K2->Left = K1->Right;
    K1->Right = K2;

    K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;

    K1->Height = Max(Height(K1->Left), Height(K1->Right)) + 1;
    
    return K1;  /* New Root */
}   

/* 右右的情况下 */
static Position SingleRotateWithRight(Position K2)
{
    Position K1;

    K1 = K2->Right;
    K2->Right = K1->Left;
    K1->Left = K2;
    
    K2->Height = Max(Height(K2->Left), Height(K2->Right)) + 1;
    
    K1->Height = Max(Height(K1->Left), Height(K1->Right)) + 1;
    
    return K1;  /* New Root */
}  

对于第三种情况（第四种类似）：

执行的变换代码为：

/* 左右情况 */
static Position DoubleRotateWithLeft(Position K3)
{
    /* Rotate between K1 and K2 */
    K3->Left = SingleRotateWithRight(K3->Left);

    /* Rotate between K3 and K2 */
    return SingleRotateWithLeft(K3);
}

/* 右左情况 */
static Position DoubleRotateWithRight(Position K3)
{
    /* Rotate between K1 and K2 */
    K3->Right = SingleRotateWithRight(K3->Right);

    /* Rotate between K3 and K2 */
    return SingleRotateWithRight(K3);
}

向AVL树中插入节点的函数：

AvlTree Insert(Element x, AvlTree T)
{
    if (T == NULL)
    {
        T = malloc(sizeof(struct AvlNode));
        if (T == NULL)
            printf("Out of space!\n");
        else
        {
            T->Element = x;
            T->Height = 0;
            T->Left = T->Right = NULL;
        }   
    }   
    else if (x < T->Element)
    {
        T->Left = Insert(x, T->Left);
        if (Height(T->Left) - Height(T->Right) == 2)
            if (x < T->Left->Element)
                T = SingleRotateWithLeft(T);
            else
                T = DoubleRotateWithLeft(T);
    }   
    else if (x > T->Element)
    {
        T->Right = Insert(x, T->Right);
        if (Height(T->Right) - Height(T->Left) == 2)
            if (x > T->Right->Element)
                T = SingleRotateWithRight(T);
            else
                T = DoubleRotateWithRight(T);
    }   
    /* Else x is in the tree already; we'll do nothing */
    T->Height = Max(Height(T->Left), Height(T->Right)) + 1;
    return T;
}