Binary Search Tree insert with Parent Pointer
We have discussed simple BST insert. How to insert in a tree where parent pointer needs to be maintained. Parent pointers are helpful to quickly find ancestors of a node, LCA of two nodes, successor of a node, etc.
In recursive calls of simple insertion, we return pointer of root of subtree created in a subtree. So the idea is to store this pointer for left and right subtrees. We set parent pointers of this returned pointers after the recursive calls. This makes sure that all parent pointers are set during insertion. Parent of root is set to NULL. We handle this by assigning parent as NULL by default to all newly allocated nodes.
C++
// C++ program to demonstrate insert operation// in binary search tree with parent pointer#include<bits/stdc++.h> struct Node{ int key; struct Node *left, *right, *parent;}; // A utility function to create a new BST Nodestruct Node *newNode(int item){ struct Node *temp = new Node; temp->key = item; temp->left = temp->right = NULL; temp->parent = NULL; return temp;} // A utility function to do inorder traversal of BSTvoid inorder(struct Node *root){ if (root != NULL) { inorder(root->left); printf("Node : %d, ", root->key); if (root->parent == NULL) printf("Parent : NULL \n"); else printf("Parent : %d \n", root->parent->key); inorder(root->right); }} /* 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 *lchild = insert(node->left, key); node->left = lchild; // Set parent of root of left subtree lchild->parent = node; } else if (key > node->key) { Node *rchild = insert(node->right, key); node->right = rchild; // Set parent of root of right subtree rchild->parent = node; } /* return the (unchanged) Node pointer */ return node;} // Driver Program to test above functionsint main(){ /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ struct Node *root = NULL; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // print iNoder traversal of the BST inorder(root); return 0;} |
Java
// Java program to demonstrate insert operation // in binary search tree with parent pointer class GfG { static class Node { int key; Node left, right, parent; } // A utility function to create a new BST Node static Node newNode(int item) { Node temp = new Node(); temp.key = item; temp.left = null; temp.right = null; temp.parent = null; return temp; } // A utility function to do inorder traversal of BST static void inorder(Node root) { if (root != null) { inorder(root.left); System.out.print("Node : "+ root.key + " , "); if (root.parent == null) System.out.println("Parent : NULL"); else System.out.println("Parent : " + root.parent.key); inorder(root.right); } } /* A utility function to insert a new Node with given key in BST */static Node insert(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 lchild = insert(node.left, key); node.left = lchild; // Set parent of root of left subtree lchild.parent = node; } else if (key > node.key) { Node rchild = insert(node.right, key); node.right = rchild; // Set parent of root of right subtree rchild.parent = node; } /* return the (unchanged) Node pointer */ return node; } // Driver Program to test above functions public static void main(String[] args) { /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ Node root = null; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // print iNoder traversal of the BST inorder(root); }} |
Python3
# Python3 program to demonstrate insert operation # in binary search tree with parent pointer # A utility function to create a new BST Node class newNode: def __init__(self, item): self.key = item self.left = self.right = None self.parent = None # A utility function to do inorder # traversal of BST def inorder(root): if root != None: inorder(root.left) print("Node :", root.key, ", ", end = "") if root.parent == None: print("Parent : NULL") else: print("Parent : ", root.parent.key) inorder(root.right) # A utility function to insert a new # Node with given key in BST def insert(node, key): # If the tree is empty, return a new Node if node == None: return newNode(key) # Otherwise, recur down the tree if key < node.key: lchild = insert(node.left, key) node.left = lchild # Set parent of root of left subtree lchild.parent = node elif key > node.key: rchild = insert(node.right, key) node.right = rchild # Set parent of root of right subtree rchild.parent = node # return the (unchanged) Node pointer return node # Driver Codeif __name__ == '__main__': # Let us create following BST # 50 # / \ # 30 70 # / \ / \ # 20 40 60 80 root = None root = insert(root, 50) insert(root, 30) insert(root, 20) insert(root, 40) insert(root, 70) insert(root, 60) insert(root, 80) # print iNoder traversal of the BST inorder(root) # This code is contributed by PranchalK |
C#
// C# program to demonstrate insert operation // in binary search tree with parent pointer using System; class GfG { class Node { public int key; public Node left, right, parent; } // A utility function to create a new BST Node static Node newNode(int item) { Node temp = new Node(); temp.key = item; temp.left = null; temp.right = null; temp.parent = null; return temp; } // A utility function to do // inorder traversal of BST static void inorder(Node root) { if (root != null) { inorder(root.left); Console.Write("Node : "+ root.key + " , "); if (root.parent == null) Console.WriteLine("Parent : NULL"); else Console.WriteLine("Parent : " + root.parent.key); inorder(root.right); } } /* A utility function to insert a new Node with given key in BST */ static Node insert(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 lchild = insert(node.left, key); node.left = lchild; // Set parent of root of left subtree lchild.parent = node; } else if (key > node.key) { Node rchild = insert(node.right, key); node.right = rchild; // Set parent of root of right subtree rchild.parent = node; } /* return the (unchanged) Node pointer */ return node; } // Driver code public static void Main(String[] args) { /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ Node root = null; root = insert(root, 50); insert(root, 30); insert(root, 20); insert(root, 40); insert(root, 70); insert(root, 60); insert(root, 80); // print iNoder traversal of the BST inorder(root); } } // This code is contributed 29AjayKumar |
Output :
Node : 20, Parent : 30 Node : 30, Parent : 50 Node : 40, Parent : 30 Node : 50, Parent : NULL Node : 60, Parent : 70 Node : 70, Parent : 50 Node : 80, Parent : 70
Exercise:
How to maintain parent pointer during deletion.
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