Merge two BSTs with constant extra space
Given two Binary Search Trees(BST), print the elements of both BSTs in sorted form.
Note: Both the BSTs will not have any common element.
Examples:
Input
First BST:
3
/ \
1 5
Second BST:
4
/ \
2 6
Output: 1 2 3 4 5 6
Input:
First BST:
8
/ \
2 10
/
1
Second BST:
5
/
3
/
0
Output: 0 1 2 3 5 8 10
The idea is to use the fact the leftmost element (first in inorder traversal) of the tree is the least element in a BST. So we compute this value for both the trees and print the smaller one, now we delete this printed element from the respective tree and update it. Then we recursively call our function with the updated tree. We do this until one of the trees is exhausted. Now we simply print the inorder traversal of the other tree.
Below is the implementation of above approach:
C++
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std;// Structure of a BST Nodeclass Node {public: int data; Node* left; Node* right; Node(int x) { data = x; left = right = NULL; }};// A utility function to print// Inorder traversal of a Binary Treevoid inorder(Node* root){ if (root != NULL) { inorder(root->left); cout << root->data << " "; inorder(root->right); }}// The function to print data// of two BSTs in sorted ordervoid merge(Node* root1, Node* root2){ // Base cases if (!root1 && !root2) return; // If the first tree is exhausted // simply print the inorder // traversal of the second tree if (!root1) { inorder(root2); return; } // If second tree is exhausted // simply print the inoreder // traversal of the first tree if (!root2) { inorder(root1); return; } // A temporary pointer currently // pointing to root of first tree Node* temp1 = root1; // previous pointer to store the // parent of temporary pointer Node* prev1 = NULL; // Traverse through the first tree until you reach // the leftmost element, which is the first element // of the tree in the inorder traversal. // This is the least element of the tree while (temp1->left) { prev1 = temp1; temp1 = temp1->left; } // Another temporary pointer currently // pointing to root of second tree Node* temp2 = root2; // Previous pointer to store the // parent of second temporary pointer Node* prev2 = NULL; // Traverse through the second tree until you reach // the leftmost element, which is the first element of // the tree in inorder traversal. // This is the least element of the tree. while (temp2->left) { prev2 = temp2; temp2 = temp2->left; } // Compare the least current least // elements of both the tree if (temp1->data <= temp2->data) { // If first tree's element is smaller print it cout << temp1->data << " "; // If the node has no parent, that // means this node is the root if (prev1 == NULL) { // Simply make the right // child of the root as new root merge(root1->right, root2); } // If node has a parent else { // As this node is the leftmost node, // it is certain that it will not have // a let child so we simply assign this // node's right pointer, which can be // either null or not, to its parent's left // pointer. This statement is // just doing the task of deleting the node prev1->left = temp1->right; // recursively call the merge // function with updated tree merge(root1, root2); } } else { cout << temp2->data << " "; // If the node has no parent, that // means this node is the root if (prev2 == NULL) { // Simply make the right child // of root as new root merge(root1, root2->right); } // If node has a parent else { prev2->left = temp2->right; // Recursively call the merge // function with updated tree merge(root1, root2); } }}// Driver Codeint main(){ Node *root1 = NULL, *root2 = NULL; root1 = new Node(3); root1->left = new Node(1); root1->right = new Node(5); root2 = new Node(4); root2->left = new Node(2); root2->right = new Node(6); // Print sorted nodes of both trees merge(root1, root2); return 0;} |
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Java
// Java implementation of above approachimport java.util.*;class GFG{ // Structure of a BST Nodestatic class Node { int data; Node left; Node right;};static Node newNode(int num) { Node temp = new Node(); temp.data = num; temp.left = temp.right = null; return temp; } // A utility function to print// Inorder traversal of a Binary Treestatic void inorder(Node root){ if (root != null) { inorder(root.left); System.out.print(root.data + " "); inorder(root.right); }}// The function to print data// of two BSTs in sorted orderstatic void merge(Node root1, Node root2){ // Base cases if (root1 == null && root2 == null) return; // If the first tree is exhausted // simply print the inorder // traversal of the second tree if (root1 == null) { inorder(root2); return; } // If second tree is exhausted // simply print the inoreder // traversal of the first tree if (root2 == null) { inorder(root1); return; } // A temporary pointer currently // pointing to root of first tree Node temp1 = root1; // previous pointer to store the // parent of temporary pointer Node prev1 = null; // Traverse through the first tree // until you reach the leftmost element, // which is the first element of the tree // in the inorder traversal. // This is the least element of the tree while (temp1.left != null) { prev1 = temp1; temp1 = temp1.left; } // Another temporary pointer currently // pointing to root of second tree Node temp2 = root2; // Previous pointer to store the // parent of second temporary pointer Node prev2 = null; // Traverse through the second tree // until you reach the leftmost element, // which is the first element of // the tree in inorder traversal. // This is the least element of the tree. while (temp2.left != null) { prev2 = temp2; temp2 = temp2.left; } // Compare the least current least // elements of both the tree if (temp1.data <= temp2.data) { // If first tree's element is // smaller print it System.out.print(temp1.data + " "); // If the node has no parent, that // means this node is the root if (prev1 == null) { // Simply make the right // child of the root as new root merge(root1.right, root2); } // If node has a parent else { // As this node is the leftmost node, // it is certain that it will not have // a let child so we simply assign this // node's right pointer, which can be // either null or not, to its parent's left // pointer. This statement is // just doing the task of deleting the node prev1.left = temp1.right; // recursively call the merge // function with updated tree merge(root1, root2); } } else { System.out.print(temp2.data + " "); // If the node has no parent, that // means this node is the root if (prev2 == null) { // Simply make the right child // of root as new root merge(root1, root2.right); } // If node has a parent else { prev2.left = temp2.right; // Recursively call the merge // function with updated tree merge(root1, root2); } }}// Driver Codepublic static void main(String args[]){ Node root1 = null, root2 = null; root1 = newNode(3); root1.left = newNode(1); root1.right = newNode(5); root2 = newNode(4); root2.left = newNode(2); root2.right = newNode(6); // Print sorted nodes of both trees merge(root1, root2);}}// This code is contributed by ipg2016107 |
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Python3
# Python3 implementation of above approach# Node of the binary treeclass node: def __init__ (self, key): self.data = key self.left = None self.right = None# A utility function to print# Inorder traversal of a Binary Treedef inorder(root): if (root != None): inorder(root.left) print(root.data, end = " ") inorder(root.right)# The function to print data# of two BSTs in sorted orderdef merge(root1, root2): # Base cases if (not root1 and not root2): return # If the first tree is exhausted # simply print the inorder # traversal of the second tree if (not root1): inorder(root2) return # If second tree is exhausted # simply print the inoreder # traversal of the first tree if (not root2): inorder(root1) return # A temporary pointer currently # pointing to root of first tree temp1 = root1 # previous pointer to store the # parent of temporary pointer prev1 = None # Traverse through the first tree # until you reach the leftmost # element, which is the first element # of the tree in the inorder traversal. # This is the least element of the tree while (temp1.left): prev1 = temp1 temp1 = temp1.left # Another temporary pointer currently # pointing to root of second tree temp2 = root2 # Previous pointer to store the # parent of second temporary pointer prev2 = None # Traverse through the second tree # until you reach the leftmost element, # which is the first element of the # tree in inorder traversal. This is # the least element of the tree. while (temp2.left): prev2 = temp2 temp2 = temp2.left # Compare the least current least # elements of both the tree if (temp1.data <= temp2.data): # If first tree's element is # smaller print it print(temp1.data, end = " ") # If the node has no parent, that # means this node is the root if (prev1 == None): # Simply make the right # child of the root as new root merge(root1.right, root2) # If node has a parent else: # As this node is the leftmost node, # it is certain that it will not have # a let child so we simply assign this # node's right pointer, which can be # either null or not, to its parent's left # pointer. This statement is # just doing the task of deleting the node prev1.left = temp1.right # recursively call the merge # function with updated tree merge(root1, root2) else: print(temp2.data, end = " ") # If the node has no parent, that # means this node is the root if (prev2 == None): # Simply make the right child # of root as new root merge(root1, root2.right) # If node has a parent else: prev2.left = temp2.right # Recursively call the merge # function with updated tree merge(root1, root2)# Driver Codeif __name__ == '__main__': root1 = None root2 = None root1 = node(3) root1.left = node(1) root1.right = node(5) root2 = node(4) root2.left = node(2) root2.right = node(6) # Print sorted nodes of both trees merge(root1, root2)# This code is contributed by mohit kumar 29 |
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Output:
1 2 3 4 5 6
Time Complexity: O((M+N)(h1+h2)), where M and N are the number of nodes of the two trees and, h1 and h2 are the heights of tree respectively.
Auxiliary Space: O(1)
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