The tree's stretching tree

What does this article introduce?

1. What is the effect of using a stretching tree;
   

2. The definition of a stretching tree;

3. The description of the concrete implementation process of the extensional tree ADT;

4. Code implementation.

The effect of using a stretch tree (splay trees):

When using the stretch tree, the worst run time for any operation on the stretch tree is O (N), but it guarantees that the maximum time for a continuous M operation is O (m㏒n), so that the amortization time for each operation of the stretch tree can be calculated as O (㏒n).

Second, the definition of stretching tree:

For a binary lookup tree operation, each access node is placed on the root by a rotation operation. Such a binary search tree is called a stretch tree.

Iii. description of the extensional tree ADT:

1. The node definition of the extension tree is consistent with the method defined by the two lookup tree nodes, which is not mentioned here;

2. Compared to the two search tree, the stretch tree ADT is just a rotation operation. Here's the spin that we call the unfold (splaying). Set node x as the Access node, we move node x to the root node by a series of operations on Node X.

3. Node x rotation Condition:

⑴ node x is the root node: do nothing;

The parent node of ⑵ node x is the root node:

The right sub-tree of the left subtree of the root node =x;

Right sub-tree of x = root node;

⑶ node x has a parent node (P), a grandparent node (G), and there are (class two) four scenarios to consider:

Ⅰ, ("one" glyph) p is the left son of G, X is the left son of P;

Ⅱ, ("one" glyph) p is the right son of G, X is the right son of P;

Ⅲ, ("the" glyph) p is the left son of G, X is the right son of P;

Ⅳ, ("the" glyph) p is the right son of G, X is the left son of P;

4. Deletion of nodes:

Because every access to node x needs to move x to the root node, lazy deletion is inappropriate here, and it needs to be removed directly here. When the delete operation, the first need to access node X, node x is moved to the root node, at this time the cost of deleting x is relatively small. When deleting node x, ① Access x causes node x to be moved to the root node, delete node x and get left and right two subtrees trees (TL, TR); ② accesses the minimum node Y on the right subtree TR (the node must have no left son), moves y to the root of the right subtree, and ③ leaves the left son of Y as the left dial hand tree TL

Four, the core code implementation:

1. Stretching the tree to achieve

Ⅰ, ("one" glyph) p is the left son of G, X is the left son of P;

Operation:

The right son of =p, the left son of G;

P's right son =g;

P's left son =x's right son;

X's right son =p;

One glyph (left left) static Position Zigzigll (Position g) {Position p,x;        p=g->left;x=p->left;    g->left=p->right;    p->right=g;    p->left=x->right;        x->right=p; return x;}

Ⅱ, ("one" glyph) p is the right son of G, X is the right son of P;

Operation:

G's right son =p's left son;

P's left son =g;

P's right son =x's left son;

X's left son =p;

One glyph (right-right) static Position Zigzigrr (Position g) {Position p,x;        p=g->right;x=p->right;    g->right=p->left;    p->left=g;    p->right=x->left;        x->left=p; return x;}

Ⅲ, ("the" glyph) p is the left son of G, X is the right son of P;

Operation:

The right son of =x, the left son of G;

X's right son =g;

P's right son =x's left son;

X's left son =p;

One glyph (left and right) static Position ZIGZIGLR (Position g) {Position p,x;        p=g->left;x=p->right;    g->left=x->right;    x->right=g;    p->right=x->left;        x->left=p; return x;}

Ⅳ, ("the" glyph) p is the right son of G, X is the left son of P;

Operation:

G's right son =x's left son;

X's left son =g;

P's left son =x's right son;

X's right son =p;

One glyph (right left) static Position Zigzigrl (Position g) {Position p,x;        p=g->right;x=p->left;    g->right=x->left;    x->left=g;    p->left=x->right;        x->right=p; return x;}

3. Implementation of the delete operation of the stretching tree

Delete the node void Delete (const ElementType X,const Stree St) {if (null==st) printf ("The tree is empty tree \ n");        else{position Temp=find (x,st);        Position root=findmin (temp->right);                root->left=temp->left;        Free (temp);        Temp=null;    return; }}

The tree's stretching tree