Chapter - Tree Basic tree concepts Binary trees Binary Search Tree (BST) 10 Delete node from BST • Node having both subtrees 74 Delete node from BST Auxiliary functions for Insert: recursive_Delete iterative_Delete 75 Recursive Delete recursive_Delete (ref subroot , val key ) Deletes a node from a BST Pre subroot is NULL or points to the root of a subtree Key contains value needs to be removed from BST Post If key is found, it will be removed from BST Return notFound or success Uses recursive_Delete and RemoveNode functions 76 Recursive Delete (cont.) recursive_Delete (ref subroot , val key ) if (subroot is NULL) return notFound else if (key < subroot->data.key) return recursive_Delete(subroot->left, key) else if (key > subroot->data.key) return recursive_Delete(subroot->right, key) else RemoveNode(subroot) return success End recursive_Delete 77 Delete Node from BST Delete (val key ) Deletes a node from a BST Pre subroot is NULL or points to the root of a subtree Key contains value needs to be removed from BST Post If key is found, it will be removed from BST Return notFound or success Uses recursive_Delete and RemoveNode functions return recursive_Delete (root, key) End Delete 78 Auxiliary Function RemoveNode RemoveNode (ref subroot , val key ) pDel = subroot // remember node to delete at end if (subroot ->left is NULL) // leaf node or node having only right subtree subroot = subroot->right // (a) and (b) else if (subroot->right is NULL) // node having only left subtree subroot = subroot->left subroot pDel subroot pDel (a) key needs to be deleted = 18 (b) 79 Auxiliary Function RemoveNode RemoveNode (ref subroot , val key ) pDel = subroot // remember node to delete at end if (subroot ->left is NULL) // leaf node or node having only right subtree subroot = subroot->right // (a) and (b) else if (subroot->right is NULL) // node having only left subtree subroot = subroot->left subroot pDel subroot pDel (a) key needs to be deleted = 18 key needs to be deleted = 18 (b) 80 Auxiliary Function RemoveNode RemoveNode (ref subroot , val key ) pDel = subroot // remember node to delete at end if (subroot ->left is NULL) // leaf node or node having only right subtree subroot = subroot->right else if (subroot->right is NULL) // node having only left subtree subroot = subroot->left // (c) subroot pDel key needs to be deleted = 44 (c) 81 Auxiliary Function RemoveNode RemoveNode (ref subroot , val key ) pDel = subroot // remember node to delete at end if (subroot ->left is NULL) // leaf node or node having only right subtree subroot = subroot->right else if (subroot->right is NULL) // node having only left subtree subroot = subroot->left // (c) subroot pDel key needs to be deleted = 44 (c) 82 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot parent if (parent = subroot) parent->left = pDel->left pDel else parent->right = pDel->left recycle pDel End RemoveNode (d) 83 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot if (parent = subroot) parent->left = pDel->left parent else parent->right = pDel->left pDel recycle pDel return success End RemoveNode (d) 84 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot if (parent = subroot) parent->left = pDel->left else parent->right = pDel->left parent recycle pDel return success End RemoveNode pDel (d) 85 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot if (parent = subroot) parent->left = pDel->left else parent->right = pDel->left parent recycle pDel return success End RemoveNode pDel 22 (d) 86 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot if (parent = subroot) 22 parent->left = pDel->left else parent->right = pDel->left parent recycle pDel return success End RemoveNode pDel 22 (d) 87 Auxiliary Function RemoveNode (cont.) else // node having both subtrees (d) parent = subroot pDel = parent ->left // move left to find the predecessor loop (pDel->right is not NULL) // pDel is not the predecessor parent = pDel key needs to be deleted = 23 pDel = pDel->right subroot->data = pDel->data subroot if (parent = subroot) 22 parent->left = pDel->left else parent->right = pDel->left parent recycle pDel return success pDel End RemoveNode (d) 88 ... not NULL) AND (subroot- >data. key target) if (target < subroot- >data. key) subroot = subroot->left else subroot = subroot->right return subroot End iterative_Search Target = 22 subroot 47 Search... (refOperation(ref Data )) inOrderTraverse (refOperation(ref Data )) postOrderTraverse (refOperation(ref Data )) • Breadth-First Traverse:... recursive_postOrder(subroot->left) recursive_postOrder(subroot->right) Operation(subroot- >data) End recursive_postOrder 30 Depth-First Traversal preOrderTraverse (refOperation(ref Data ))