Lecture 34 - Nov 30, 2023

Last lecture

BST (insert and print)

Today

Delete a node in a BST.

Node deletion in BST

class BSTNode {
  private:
    int value;
    BSTNode *left, *right;

  public:
    BSTNode(int v) { value = v; left = right = NULL; }
    ~BSTNode() { delete left; delete right; }
    int getValue() { return value; }
    BSTNode *getLeft() { return left; }
    BSTNode *getRight() { return right; }
    void setLeft(BSTNode *l) { left = l; }
    void setRight(BSTNode *r) { right = r; }
};

class BSTree {
  private:
    BSTNode *root;
    bool searchNode(int v, BSTNode *n);
    void insertHelper(int v, BSTNode *n);
    void printInOrderHelper(BSTNode *n);
    BSTNode* minValueNodeHelper(BSTNode *n);
  
  public:
    BSTree() { root = NULL; }
    ~BSTree() { delete root; }
    BSTNode* getRoot() { return root; }
    bool search(int v);
    void insert(int v);
    void printInOrder();
    BSTNode* minValueNode();
};

BSTNode* BSTree::minValueNode() {
  return minValueNodeHelper(root);
}

BSTNode* BSTree::minValueNodeHelper(BSTNode* p) {
  // p != NULL in case the root is NULL
  if (p != NULL && p->getLeft() != NULL) {
    return minValueNodeHelper(p->getLeft());
  } else {
    return p;
  }
}

To delete a node in a BST, we have to make sure the properties of a BST are maintained when the node is removed.

Find the node
If the node has no children, delete node and update parent node pointer

     8
   /   \
  3     10
 / \      \
1   6      14
   / \    /
  4   7 13

For example, nodes 1, 4, 7 and 13.

If the node has only one subtree, make the parent node point to the parent of the subtree

For example, nodes 10 and 14.

If the node has two subtrees, replace the node data with the minimum in the right subtree, delete the node with the minimum value in the right subtree

For example, delete 3.

     8
   /   \
  4     10
 / \      \
1   6      14
     \    /
      7 13

Could 4 have children? Yes, in the right subtree. Delete 4 by calling the delete node function on 4.

     8
   /   \
  4     10
 / \      \
1   6      14
   / \    /
  5   7 13

BSTNode* BSTree::deleteNode(int v, BSTNode* node) {
  if (node == NULL) {
    return node;
  }

  if (v < node->getValue()) {
    node->setLeft(deleteNode(v, node->getLeft()));
  } else if (v > node->getValue()) {
    node->setRight(deleteNode(v, node->getRight()));
  } else {
    // one or no children
    if (node->getLeft() == NULL) {
      BSTNode* temp = node->getRight();
      node->setRight(NULL);
      delete node;
      return temp; // want to put it in the BST back
    } else if (node->getRight() == NULL) {
      // one child on left
      BSTNode* temp = node->getLeft();
      delete node;
      return temp; // we want to put it in the BST back
    } else {
      // node has two children
      BSTNode* temp = minValue(node->getRight());
      node->setValue(temp->getValue());
      // look in the right subtree
      node->setRight(deleteNode(temp->getValue(), node->getRight()));
    }
  }

  return node;
}

Trace:

Before

After