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binary search tree delete

abdelouafiDec 1, 2017

    1. abdelouafi

      abdelouafi Administrator Staff Member

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      Sep 13, 2016
      binary search tree delete:

      We have discussed BST search and insert operations. In this post, delete operation is discussed. When we delete a node, there possibilities arise.


      // C program to demonstrate delete operation in binary search tree
      struct node
          int key;
          struct node *left, *right;
      // A utility function to create a new BST node
      struct node *newNode(int item)
          struct node *temp =  (struct node *)malloc(sizeof(struct node));
          temp->key = item;
          temp->left = temp->right = NULL;
          return temp;
      // A utility function to do inorder traversal of BST
      void inorder(struct node *root)
          if (root != NULL)
              printf("%d ", root->key);
      /* A utility function to insert a new node with given key in BST */
      struct node* insert(struct node* node, int key)
          /* If the tree is empty, return a new node */
          if (node == NULL) return newNode(key);
          /* Otherwise, recur down the tree */
          if (key < node->key)
              node->left  = insert(node->left, key);
              node->right = insert(node->right, key);
          /* return the (unchanged) node pointer */
          return node;
      /* Given a non-empty binary search tree, return the node with minimum
         key value found in that tree. Note that the entire tree does not
         need to be searched. */
      struct node * minValueNode(struct node* node)
          struct node* current = node;
          /* loop down to find the leftmost leaf */
          while (current->left != NULL)
              current = current->left;
          return current;
      /* Given a binary search tree and a key, this function deletes the key
         and returns the new root */
      struct node* deleteNode(struct node* root, int key)
          // base case
          if (root == NULL) return root;
          // If the key to be deleted is smaller than the root's key,
          // then it lies in left subtree
          if (key < root->key)
              root->left = deleteNode(root->left, key);
          // If the key to be deleted is greater than the root's key,
          // then it lies in right subtree
          else if (key > root->key)
              root->right = deleteNode(root->right, key);
          // if key is same as root's key, then This is the node
          // to be deleted
              // node with only one child or no child
              if (root->left == NULL)
                  struct node *temp = root->right;
                  return temp;
              else if (root->right == NULL)
                  struct node *temp = root->left;
                  return temp;
              // node with two children: Get the inorder successor (smallest
              // in the right subtree)
              struct node* temp = minValueNode(root->right);
              // Copy the inorder successor's content to this node
              root->key = temp->key;
              // Delete the inorder successor
              root->right = deleteNode(root->right, temp->key);
          return root;
      // Driver Program to test above functions
      int main()
          /* Let us create following BST
                 /     \
                30      70
               /  \    /  \
             20   40  60   80 */
          struct node *root = NULL;
          root = insert(root, 50);
          root = insert(root, 30);
          root = insert(root, 20);
          root = insert(root, 40);
          root = insert(root, 70);
          root = insert(root, 60);
          root = insert(root, 80);
          printf("Inorder traversal of the given tree \n");
          printf("\nDelete 20\n");
          root = deleteNode(root, 20);
          printf("Inorder traversal of the modified tree \n");
          printf("\nDelete 30\n");
          root = deleteNode(root, 30);
          printf("Inorder traversal of the modified tree \n");
          printf("\nDelete 50\n");
          root = deleteNode(root, 50);
          printf("Inorder traversal of the modified tree \n");
          return 0;


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