Replace each node in binary tree with the sum of its inorder predecessor and successor
Given a binary tree containing n nodes. The problem is to replace each node in the binary tree with the sum of its inorder predecessor and inorder successor.
Examples:
Input : 1
/ \
2 3
/ \ / \
4 5 6 7
Output : 11
/ \
9 13
/ \ / \
2 3 4 3
For 1:
Inorder predecessor = 5
Inorder successor = 6
Sum = 11
For 4:
Inorder predecessor = 0
(as inorder predecessor is not present)
Inorder successor = 2
Sum = 2
For 7:
Inorder predecessor = 3
Inorder successor = 0
(as inorder successor is not present)
Sum = 3
Approach: Create an array arr. Store 0 at index 0. Now, store the inorder traversal of tree in the array arr. Then, store 0 at last index. 0’s are stored as inorder predecessor of leftmost leaf and inorder successor of rightmost leaf is not present. Now, perform inorder traversal and while traversing node replace node’s value with arr[i-1] + arr[i+1] and then increment i. In the beginning initialize i = 1. For an element arr[i], the values arr[i-1] and arr[i+1] are its inorder predecessor and inorder successor respectively.
C++
// C++ implementation to replace each node // in binary tree with the sum of its inorder // predecessor and successor #include <bits/stdc++.h> using namespace std; // node of a binary tree struct Node { int data; struct Node* left, *right; }; // function to get a new node of a binary tree struct Node* getNode(int data) { // allocate node struct Node* new_node = (struct Node*)malloc(sizeof(struct Node)); // put in the data; new_node->data = data; new_node->left = new_node->right = NULL; return new_node; } // function to store the inorder traversal // of the binary tree in 'arr' void storeInorderTraversal(struct Node* root, vector<int>& arr) { // if root is NULL if (!root) return; // first recur on left child storeInorderTraversal(root->left, arr); // then store the root's data in 'arr' arr.push_back(root->data); // now recur on right child storeInorderTraversal(root->right, arr); } // function to replace each node with the sum of its // inorder predecessor and successor void replaceNodeWithSum(struct Node* root, vector<int> arr, int* i) { // if root is NULL if (!root) return; // first recur on left child replaceNodeWithSum(root->left, arr, i); // replace node's data with the sum of its // inorder predecessor and successor root->data = arr[*i - 1] + arr[*i + 1]; // move 'i' to point to the next 'arr' element ++*i; // now recur on right child replaceNodeWithSum(root->right, arr, i); } // Utility function to replace each node in binary // tree with the sum of its inorder predecessor // and successor void replaceNodeWithSumUtil(struct Node* root) { // if tree is empty if (!root) return; vector<int> arr; // store the value of inorder predecessor // for the leftmost leaf arr.push_back(0); // store the inoder traversal of the tree in 'arr' storeInorderTraversal(root, arr); // store the value of inorder successor // for the rightmost leaf arr.push_back(0); // replace each node with the required sum int i = 1; replaceNodeWithSum(root, arr, &i); } // function to print the preorder traversal // of a binary tree void preorderTraversal(struct Node* root) { // if root is NULL if (!root) return; // first print the data of node cout << root->data << " "; // then recur on left subtree preorderTraversal(root->left); // now recur on right subtree preorderTraversal(root->right); } // Driver program to test above int main() { // binary tree formation struct Node* root = getNode(1); /* 1 */ root->left = getNode(2); /* / \ */ root->right = getNode(3); /* 2 3 */ root->left->left = getNode(4); /* / \ / \ */ root->left->right = getNode(5); /* 4 5 6 7 */ root->right->left = getNode(6); root->right->right = getNode(7); cout << "Preorder Traversal before tree modification:n"; preorderTraversal(root); replaceNodeWithSumUtil(root); cout << "\nPreorder Traversal after tree modification:n"; preorderTraversal(root); return 0; } |
Java
// Java implementation to replace each node // in binary tree with the sum of its inorder // predecessor and successor import java.util.*; class Solution { // node of a binary tree static class Node { int data; Node left, right; } //INT class static class INT { int data; } // function to get a new node of a binary tree static Node getNode(int data) { // allocate node Node new_node =new Node(); // put in the data; new_node.data = data; new_node.left = new_node.right = null; return new_node; } // function to store the inorder traversal // of the binary tree in 'arr' static void storeInorderTraversal( Node root, Vector<Integer> arr) { // if root is null if (root==null) return; // first recur on left child storeInorderTraversal(root.left, arr); // then store the root's data in 'arr' arr.add(root.data); // now recur on right child storeInorderTraversal(root.right, arr); } // function to replace each node with the sum of its // inorder predecessor and successor static void replaceNodeWithSum( Node root, Vector<Integer> arr, INT i) { // if root is null if (root==null) return; // first recur on left child replaceNodeWithSum(root.left, arr, i); // replace node's data with the sum of its // inorder predecessor and successor root.data = arr.get(i.data - 1) + arr.get(i.data + 1); // move 'i' to point to the next 'arr' element i.data++; // now recur on right child replaceNodeWithSum(root.right, arr, i); } // Utility function to replace each node in binary // tree with the sum of its inorder predecessor // and successor static void replaceNodeWithSumUtil( Node root) { // if tree is empty if (root==null) return; Vector<Integer> arr= new Vector<Integer>(); // store the value of inorder predecessor // for the leftmost leaf arr.add(0); // store the inoder traversal of the tree in 'arr' storeInorderTraversal(root, arr); // store the value of inorder successor // for the rightmost leaf arr.add(0); // replace each node with the required sum INT i = new INT(); i.data=1; replaceNodeWithSum(root, arr, i); } // function to print the preorder traversal // of a binary tree static void preorderTraversal( Node root) { // if root is null if (root==null) return; // first print the data of node System.out.print( root.data + " "); // then recur on left subtree preorderTraversal(root.left); // now recur on right subtree preorderTraversal(root.right); } // Driver program to test above public static void main(String args[]) { // binary tree formation Node root = getNode(1); // 1 root.left = getNode(2); // / \ root.right = getNode(3); // 2 3 root.left.left = getNode(4); // / \ / \ root.left.right = getNode(5); // 4 5 6 7 root.right.left = getNode(6); root.right.right = getNode(7); System.out.println( "Preorder Traversal before tree modification:"); preorderTraversal(root); replaceNodeWithSumUtil(root); System.out.println("\nPreorder Traversal after tree modification:"); preorderTraversal(root); } } //contributed by Arnab Kundu |
Python3
# Python3 implementation to replace each # node in binary tree with the sum of its # inorder predecessor and successor # class to get a new node of a # binary tree class getNode: def __init__(self, data): # put in the data self.data = data self.left = self.right = None # function to store the inorder traversal # of the binary tree in 'arr' def storeInorderTraversal(root, arr): # if root is None if (not root): return # first recur on left child storeInorderTraversal(root.left, arr) # then store the root's data in 'arr' arr.append(root.data) # now recur on right child storeInorderTraversal(root.right, arr) # function to replace each node with the # sum of its inorder predecessor and successor def replaceNodeWithSum(root, arr, i): # if root is None if (not root): return # first recur on left child replaceNodeWithSum(root.left, arr, i) # replace node's data with the sum of its # inorder predecessor and successor root.data = arr[i[0] - 1] + arr[i[0] + 1] # move 'i' to poto the next 'arr' element i[0] += 1 # now recur on right child replaceNodeWithSum(root.right, arr, i) # Utility function to replace each node in # binary tree with the sum of its inorder # predecessor and successor def replaceNodeWithSumUtil(root): # if tree is empty if (not root): return arr = [] # store the value of inorder predecessor # for the leftmost leaf arr.append(0) # store the inoder traversal of the # tree in 'arr' storeInorderTraversal(root, arr) # store the value of inorder successor # for the rightmost leaf arr.append(0) # replace each node with the required sum i = [1] replaceNodeWithSum(root, arr, i) # function to print the preorder traversal # of a binary tree def preorderTraversal(root): # if root is None if (not root): return # first print the data of node print(root.data, end = " ") # then recur on left subtree preorderTraversal(root.left) # now recur on right subtree preorderTraversal(root.right) # Driver Code if __name__ == '__main__': # binary tree formation root = getNode(1) # 1 root.left = getNode(2) # / \ root.right = getNode(3) # 2 3 root.left.left = getNode(4) # / \ / \ root.left.right = getNode(5) # 4 5 6 7 root.right.left = getNode(6) root.right.right = getNode(7) print("Preorder Traversal before", "tree modification:") preorderTraversal(root) replaceNodeWithSumUtil(root) print() print("Preorder Traversal after", "tree modification:") preorderTraversal(root) # This code is contributed by PranchalK |
C#
// C# implementation to replace each // node in binary tree with the sum // of its inorder predecessor and successor using System; using System.Collections.Generic; class GFG { // node of a binary tree public class Node { public int data; public Node left, right; } // INT class public class INT { public int data; } // function to get a new node // of a binary tree public static Node getNode(int data) { // allocate node Node new_node = new Node(); // put in the data; new_node.data = data; new_node.left = new_node.right = null; return new_node; } // function to store the inorder traversal // of the binary tree in 'arr' public static void storeInorderTraversal(Node root, List<int> arr) { // if root is null if (root == null) { return; } // first recur on left child storeInorderTraversal(root.left, arr); // then store the root's data in 'arr' arr.Add(root.data); // now recur on right child storeInorderTraversal(root.right, arr); } // function to replace each node with // the sum of its inorder predecessor // and successor public static void replaceNodeWithSum(Node root, List<int> arr, INT i) { // if root is null if (root == null) { return; } // first recur on left child replaceNodeWithSum(root.left, arr, i); // replace node's data with the // sum of its inorder predecessor // and successor root.data = arr[i.data - 1] + arr[i.data + 1]; // move 'i' to point to the // next 'arr' element i.data++; // now recur on right child replaceNodeWithSum(root.right, arr, i); } // Utility function to replace each // node in binary tree with the sum // of its inorder predecessor and successor public static void replaceNodeWithSumUtil(Node root) { // if tree is empty if (root == null) { return; } List<int> arr = new List<int>(); // store the value of inorder // predecessor for the leftmost leaf arr.Add(0); // store the inoder traversal // of the tree in 'arr' storeInorderTraversal(root, arr); // store the value of inorder successor // for the rightmost leaf arr.Add(0); // replace each node with // the required sum INT i = new INT(); i.data = 1; replaceNodeWithSum(root, arr, i); } // function to print the preorder // traversal of a binary tree public static void preorderTraversal(Node root) { // if root is null if (root == null) { return; } // first print the data of node Console.Write(root.data + " "); // then recur on left subtree preorderTraversal(root.left); // now recur on right subtree preorderTraversal(root.right); } // Driver Code public static void Main(string[] args) { // binary tree formation Node root = getNode(1); // 1 root.left = getNode(2); // / \ root.right = getNode(3); // 2 3 root.left.left = getNode(4); // / \ / \ root.left.right = getNode(5); // 4 5 6 7 root.right.left = getNode(6); root.right.right = getNode(7); Console.WriteLine("Preorder Traversal " + "before tree modification:"); preorderTraversal(root); replaceNodeWithSumUtil(root); Console.WriteLine("\nPreorder Traversal after " + "tree modification:"); preorderTraversal(root); } } // This code is contributed by Shrikant13 |
Output:
Preorder Traversal before tree modification: 1 2 4 5 3 6 7 Preorder Traversal after tree modification: 11 9 2 3 13 4 3
Time Complexity: O(n)
Auxiliary Space: O(n)
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