Introduction to Algorithms Part3: two-fork search tree

1. Concept

Binary Search Tree Properties: Set X is a node of a two-fork search tree, then:

A) x record any node y, Y.key < X.key

b) Y.key >= X.key of any node y in the right sub-tree of X

2. Data structure

1 structTreeNode2 {3TreeNode (intkey): Left (null), Right (NULL), parent (null), key (key) {};4treenode*Left ;5treenode*Right ;6treenode*parent;7     intkey;8 };9 Ten classTree One { A  Public: - Tree (): M_root (NULL) {}; -treenode* Minimum (treenode* ); thetreenode* Maximum (treenode* ); -     voidCreat (intKeys[],intn); -     intInsertintkey); -     intRemoveintkey); +Treenode* Search (intkey); -     voidWalk (TreeNode *root); +treenode* Get_root ()Const; A  at protected: -Inline treenode* node_creat (intkey); -     voidTransplant (treenode* x, TreeNode *y); -  - Private: -treenode*M_root; in};

3. Algorithm

3.1 Traversal

By the nature of the two-fork search tree, the result of the middle sequence traversal is the ordered arrangement of keys

1 void Tree::walk (TreeNode *root)2{3     if (root = NULL)4          return; 5     Walk (root-> left); 6     " " ; 7     Walk (root-> right); 8 }

3.2 Maximum/Minimum value

1treenode* Tree::minimum (TreeNode *root)2 {3TreeNode *visit =Root;4     if(Visit = =NULL)5         returnNULL;6      while(Visit->left! =NULL)7Visit = visit->Left ;8     returnvisit;9 }Ten  Onetreenode* Tree::maximum (treenode*root) A { -TreeNode *visit =Root; -     if(Visit = =NULL) the         returnNULL; -      while(Visit->right! =NULL) -Visit = visit->Right ; -     returnvisit; +}

3.3 Find

1treenode* Tree::search (intkey)2 {3treenode* visit =M_root;4 5      while(Visit! =NULL)6     {7         if(Key = = Visit->key)8             returnvisit;9         if(Key < Visit->key)TenVisit = visit->Left ; One         Else AVisit = visit->Right ; -     } -  the     returnvisit; -}

3.4 Inserting

When inserted, it must be inserted into a leaf node, not between two nodes.

Find the insertion position and insert it first.

1 intTree::insert (intkey)2 {3treenode* z =NewTreeNode (key);4treenode* x =M_root;5Treenode* y =NULL;6      while(X! =NULL)7     {8y =x;9         if(Z->key < x->key)Tenx = x->Left ; One         Else Ax = x->Right ; -     } -Z->parent =y; the     if(y = = NULL)//Tree is empty -M_root =Z; -     Else if(Z->key < y->key) -Y->left =Z; +     Else -Y->right =Z; +      A     return 0; at}

3.5 Delete

When deleted, the situation is more complex, for node Z to be deleted:

IF Z.left is NULL

Replace Z by Z.right

ELSE IF Z.right is NULL

Replace Z by Z.left

ELSE//Z contains left and right subtrees

Find the successor Y of Z, which is the smallest node with a key greater than Z.key, Y is in the right subtree of Z and y is not Zuozi

IF Y.parent is Z

Replace z by y, leaving Y.right

ELSE

Replace Z.right by Y,

Replace Z by y

1 //replace x by node y2 voidTree::transplant (treenode* x, TreeNode *y)3 {4     if(x->parent = = NULL)//x is root5M_root =y;6     Else if(X->parent->left = =x)7X->parent->left =y;8     Else9X->parent->right =y;Ten  One     if(Y! =NULL) AY->parent = x->parent; - } -  the intTree::remove (intkey) - { -Treenode* y =NULL; -treenode* z =search (key); +     if(Z = =NULL) -         return-1; +  A     if(Z->left = =NULL) atTransplant (Z, z->Right ); -     Else if(Z->right = =NULL) -Transplant (Z, z->Left ); -     Else -     { -y = minimum (z->Right ); in         if(Y->parent! =z) -         { toTransplant (y, y->right);//Replace y by right child +             //Let Y is the parent of Z->right -Y->right = z->Right ; theY->right->parent =y; *         } $ transplant (z, y);Panax NotoginsengY->left = z->Left ; -Y->left->parent =y; the     } +  A     return 0; the}

Tips: Source code

Introduction to Algorithms Part3: two-fork search tree