伸展树介绍 - 使用自顶向下的调整算法

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伸展树自顶向下的伸展
Node* splaytree_splay(SplayTree tree, Type key)
Node N, *l, *r, *c;
N用来表示存放左树和右树根节点的一个Node，其中N->left存放右树的根节点，N->right存放左树的根节点
l表示右树最小节点，r表示左树最大节点，在伸展的过程中，l和r不断变化，并且通过变化连接了每一轮左右树的最大和和最小节点

每一轮的调整过程：
   如果key < tree->key
       如果tree->left == NULL，结束调整
       如果key < tree->left->key
           右旋
           右旋后如果tree->left == NULL，结束调整
       连接右树
           r->left = tree; 连接
           r = tree; 更新r节点
           tree = tree->left; 更新根节点
   如果key > tree->key
       如果tree->right == NULL，结束调整
       如果key > tree->right->key
           左旋
           左旋后如果tree->right == NULL，结束调整
       连接左树
           l->right = tree; 连接
           l = tree; 更新r节点
           tree = tree->right; 更新根节点
   如果相等，结束调整

伸展结束时
l->right = tree->left; 左树的最大节点的右孩子 = 当前根的左孩子
r->left = tree->right;右树的最小节点的左孩子 = 当前根的右孩子
tree->left = N.right; 连接左树
tree->right = N.left; 连接右树

参考代码如下：

Node* splaytree_splay(SplayTree tree, Type key){    Node N, *l, *r, *c;    if (tree == NULL)         return tree;    N.left = N.right = NULL;    l = r = &N;    for (;;)    {        if (key < tree->key)        {            if (tree->left == NULL)                break;            if (key < tree->left->key)            {                c = tree->left;                           /* 01, rotate right */                tree->left = c->right;                c->right = tree;                tree = c;                if (tree->left == NULL)                     break;            }            r->left = tree;                               /* 02, link right */            r = tree;            tree = tree->left;        }        else if (key > tree->key)        {            if (tree->right == NULL)                 break;            if (key > tree->right->key)             {                c = tree->right;                          /* 03, rotate left */                tree->right = c->left;                c->left = tree;                tree = c;                if (tree->right == NULL)                     break;            }            l->right = tree;                              /* 04, link left */            l = tree;            tree = tree->right;        }        else        {            break;        }    }    l->right = tree->left;                                /* 05, assemble */    r->left = tree->right;    tree->left = N.right;    tree->right = N.left;    return tree;}

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