Binary Search Trees Deletion

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Binary Search Trees Deletion. COP 3502. Binary Search Tree - Deletion. Let’s consider several cases for Deletion: Deleting a Leaf node Deleting a node with 1 child Deleting a node with 2 children For all cases we have to identify the parent. 6. 5. 10. 13. 9. 3. 8. 12. 1. 4. 7.

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Binary Search Trees Deletion

COP 3502

Binary Search Tree - Deletion
• Let’s consider several cases for Deletion:
• Deleting a Leaf node
• Deleting a node with 1 child
• Deleting a node with 2 children
• For all cases we have to

identify the parent.

6

5

10

13

9

3

8

12

1

4

7

9

11

13

Binary Search Tree - Deletion

parent

6

• Deleting a leaf node
• Let’s say we want to delete 3
• Find the parent of 3
• which is 5
• Then what?
• free(parent->left);
• parent->left = NULL;
• or if it’s a right leaf node:
• free(parent->right);
• parent->right= NULL;

5

9

3

Binary Search Tree - Deletion
• Deleting node with 1 child
• Let’s say we want to delete 5
• We need to find the parent
• AND the sole child
• Then connect them
• temp = parent->left;
• child = temp->left;
• parent->left = child;
• free(temp);

parent

6

temp

5

9

child

3

7

12

1

4

Binary Search Tree - Deletion

6

• Deleting a node with 2 children:
• In order to maintain the BST property , we can replace the deleted node with either:
• Max in the left subtree
• OR Min in the right subtree

5

10

9

3

8

12

1

4

7

9

11

13

Binary Search Tree Deletion
• In aiding in Deletion, we will want several auxiliary functions:
• node* parent(node* root)
• Finds the parent of a given node in a binary tree.
• node* minVal(node* root), node* maxVal(node* root)
• Finds the minimum (or maximum) value in a given binary tree.
• intisLeaf(node* root)
• Determines if a node is a leaf node or not.
• inthasOnlyLeftChild(node* root),

inthasOnlyRightChild(node* root)

• Determines if a node ONLY has a left (or right) child or not.
• node* findNode(node* root)
• Returns a pointer to a node in a given tree that stores a particular value.
node* delete(node* root, int value) {

node *delnode, *parent;

// Get a pointer to the node to delete.

delnode = findNode(root, value);

// Get the parent of this node.

parent = parent(root, delnode);

// Case 1: the node to delete is a leaf node.

if (isLeaf(delnode)) {...}

// Case 2: node to be deleted only has a left child.

if (hasOnlyLeftChild(delnode)) {...}

// Case 3: node to be deleted only has a right child.

if (hasOnlyRightChild(delnode)) {...}

// Case 4: the node has 2 children

else {...}

}

Binary Search Tree Deletion
• Fill in the code together in class for the Delete function.