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Replace each node in binary tree with the sum of its inorder predecessor and successor

  • Difficulty Level : Medium
  • Last Updated : 21 Jul, 2021

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: 

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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 inorder 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 inorder 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 inorder 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 inorder 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


Javascript




<script>
 
// Javascript implementation to replace each node
// in binary tree with the sum of its inorder
// predecessor and successor
class Node
{
    constructor(data)
    {
        this.left = null;
        this.right = null;
        this.data = data;
    }
}
 
// Function to get a new node of a
// binary tree
function getNode(data)
{
     
    // Allocate node
    let new_node = new Node(data);
    return new_node;
}
 
// Function to store the inorder traversal
// of the binary tree in 'arr'
function storeInorderTraversal(root, 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.push(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
function replaceNodeWithSum(root, arr)
{
     
    // If root is null
    if (root == null)
        return;
 
    // First recur on left child
    replaceNodeWithSum(root.left, arr);
 
    // Replace node's data with the sum of its
    // inorder predecessor and successor
    root.data = arr[data - 1] + arr[data + 1];
 
    // Move 'i' to point to the next 'arr' element
    data++;
 
    // Now recur on right child
    replaceNodeWithSum(root.right, arr);
}
 
// Utility function to replace each node in binary
// tree with the sum of its inorder predecessor
// and successor
function replaceNodeWithSumUtil(root)
{
     
    // If tree is empty
    if (root == null)
        return;
 
    let arr = [];
 
    // Store the value of inorder predecessor
    // for the leftmost leaf
    arr.push(0);
 
    // Store the inorder traversal of
    // the tree in 'arr'
    storeInorderTraversal(root, arr);
 
    // Store the value of inorder successor
    // for the rightmost leaf
    arr.push(0); 
 
    // Replace each node with the required sum
    data = 1;
 
    replaceNodeWithSum(root, arr);
}
 
// Function to print the preorder traversal
// of a binary tree
function preorderTraversal(root)
{
     
    // If root is null
    if (root == null)
        return;
 
    // First print the data of node
    document.write(root.data + " ");
 
    // Then recur on left subtree
    preorderTraversal(root.left);
 
    // Now recur on right subtree
    preorderTraversal(root.right);
}
 
// Driver code
 
// Binary tree formation
let 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);
 
document.write("Preorder Traversal before " +
               "tree modification:" + "</br>");
preorderTraversal(root);
 
replaceNodeWithSumUtil(root);
 
document.write("</br>" + "Preorder Traversal after " +
               "tree modification:" + "</br>");
preorderTraversal(root);
 
// This code is contributed by divyeshrabadiya07
 
</script>


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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