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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 tree deletion
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 deletion1
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 deletion2
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 deletion3
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 deletion4
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.
slide7
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 deletion5
Binary Search Tree Deletion
  • Fill in the code together in class for the Delete function.
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