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++

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// 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;
}

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Java

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// 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

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Python3

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# 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 prthe preorder traversal 
# of a binary tree 
def preorderTraversal(root):
      
    # if root is None 
    if (not root): 
        return
  
    # first prthe 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

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C#

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// 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

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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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