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

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Binary search trees deletion

Binary Search Trees Deletion

COP 3502


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.


Binary search trees deletion

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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