Data Structure Instructor: Nabeel Alassaf Chapter 11 Binary Search Trees (Deletion by merging) Lecture 5

Transcription

1 Data Structure Instructor: Nabeel Alassaf Chapter 11 Binary Search Trees (Deletion by merging) Lecture ١

2 There are 3 cases in Deletion By Merging in your tree The Deletion depends on the Node situation as bellow : Has Left No Right Has Right No Left Has Left and Right Nabeel Alassaf: University Of Jordan,Computer Science Department,Data Structure ٢

3 Has Left No Right NodeTree *temp =node; If (node ->right == 0) { node = node->left; Delete temp; } ٣

4 Has Right No Left NodeTree *temp =node; If (node ->left== 0) { node = node->right; Delete temp; } Nabeel Alassaf: University Of Jordan,Computer Science Department,Data Structure ٤

5 Has Left and Right NodeTree *temp =node; temp=node->left; While( temp->right!=0) temp=temp->right; temp->right=node->right; temp=node; node=node->left; Delete temp; Symmetrically by left most node in Right sub tree Nabeel Alassaf: University Of Jordan,Computer Science Department,Data Structure ٥

6 example We will delete the node with the key (1). ٦

7 Template <class T> Void BST<T>::findAndDeleteByMerging (const T & el ) { BSTNode<T> * node=root,* Parent=0 ; while (node!=0){ if (node->key==el) break; Parent=node; If(node->key <el) node=node->right; else node=node->left; }//while if (node!=0 && node ->key==el) if(node==root) deletebymerging (root); else if (Parent->left==node) deletebymerging (Parent->left); else deletebymerging (Parent->right); else if (root!=0) cout<< key <<el<< is not in tree \n ; else cout<< The tree is empty \n ; } You need to find the element first by this function ٧

8 Template <class T> Void BST<T>::deleteByMerging (BSTNode<T> *& sub_root){ BSTNode<T> * tmp=sub_root; tmp 1 Sub_root ٨

9 If (sub_root!=0) { // if there is a node if (! sub_root->right ) // if it has no right child sub_root = sub_root->left; else if (sub_root->left==0) // if it has no left child Sub_root= sub_root->right; ٩

10 else{ tmp=sub_root->left; 1 Sub_root tmp ١٠

11 while (tmp->right!=0) tmp= tmp->right; 1 Sub_root tmp ١١

12 while (tmp->right!=0) tmp= tmp->right; 1 Sub_root 11 tmp 12 ١٢

13 tmp->right=sub_root->right 1 Sub_root 11 tmp 12 ١٣

14 tmp=sub_root; tmp 1 Sub_root ١٤

15 sub_root= sub_root->left; } Sub_root tmp ١٥

16 delete tmp; } } Sub_root ١٦

17 Original Tree Tree after delete 1 1 Sub_root ١٧

18 After re-arranging our BST Sub_root ١٨

19 The height of the tree can be extended or reduced after delete by merging ١٩

20 Original Tree Different between by copy and by merge ٢٠

21 After deletion by merging Sub_root Pre-order: In-order: Post-order: ٢١

22 After deletion by copy In-order: Pre-order: Post-order: ٢٢

23 Pre-order: By Copy In-order: Post-order: Pre-order: By Merge In-order: Post-order: ٢٣

24 Question? When Delete by copy and by merge yields the same tree? Sub_root ٢٤

25 tmp 1 Sub_root 4 7 ٢٥

26 Sub_root tmp ٢٦

27 Sub_root 1 tmp 4 7 ٢٧

28 tmp 1 Sub_root 4 7 ٢٨

29 tmp Sub_root ٢٩

30 Sub_root 4 7 ٣٠

31 After re-arranging the tree 4 7 ٣١

32 Pre-order: 4 7 By Copy In-order: 4 7 Post-order: 4 7 Pre-order: 4 7 By Merge In-order: 4 7 Post-order: 4 7 ٣٢