Convert a given tree to its Sum Tree

Given a Binary Tree where each node has positive and negative values. Convert this to a tree where each node contains the sum of the left and right sub trees in the original tree. The values of leaf nodes are changed to 0.

For example, the following tree  

                  10
               /      \
             -2        6
           /   \      /  \ 
         8     -4    7    5

should be changed to 

                 20(4-2+12+6)
               /      \
         4(8-4)      12(7+5)
           /   \      /  \ 
         0      0    0    0

Solution:
Do a traversal of the given tree. In the traversal, store the old value of the current node, recursively call for left and right subtrees and change the value of current node as sum of the values returned by the recursive calls. Finally return the sum of new value and value (which is sum of values in the subtree rooted with this node). 

C++

// C++ program to convert a tree into its sum tree
#include <bits/stdc++.h>
using namespace std;

/* A tree node structure */
class node
{
    public:
int data;
node *left;
node *right;
};

// Convert a given tree to a tree where
// every node contains sum of values of
// nodes in left and right subtrees in the original tree
int toSumTree(node *Node)
{
    // Base case
    if(Node == NULL)
    return 0;

    // Store the old value
    int old_val = Node->data;

    // Recursively call for left and
    // right subtrees and store the sum as
    // old value of this node
    Node->data = toSumTree(Node->left) + toSumTree(Node->right);

    // Return the sum of values of nodes
    // in left and right subtrees and
    // old_value of this node
    return Node->data + old_val;
}

// A utility function to print
// inorder traversal of a Binary Tree
void printInorder(node* Node)
{
    if (Node == NULL)
        return;
    printInorder(Node->left);
    cout<<" "<<Node->data;
    printInorder(Node->right);
}

/* Utility function to create a new Binary Tree node */
node* newNode(int data)
{
    node *temp = new node;
    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;

    return temp;
}

/* Driver code */
int main()
{
    node *root = NULL;
    int x;

    /* Constructing tree given in the above figure */
    root = newNode(10);
    root->left = newNode(-2);
    root->right = newNode(6);
    root->left->left = newNode(8);
    root->left->right = newNode(-4);
    root->right->left = newNode(7);
    root->right->right = newNode(5);

    toSumTree(root);

    // Print inorder traversal of the converted
    // tree to test result of toSumTree()
    cout<<"Inorder Traversal of the resultant tree is: \n";
    printInorder(root);
    return 0;
}

// This code is contributed by rathbhupendra

C

#include<stdio.h>

/* A tree node structure */
struct node
{
  int data;
  struct node *left;
  struct node *right;
};

// Convert a given tree to a tree where every node contains sum of values of
// nodes in left and right subtrees in the original tree
int toSumTree(struct node *node)
{
    // Base case
    if(node == NULL)
      return 0;

    // Store the old value
    int old_val = node->data;

    // Recursively call for left and right subtrees and store the sum as
    // new value of this node
    node->data = toSumTree(node->left) + toSumTree(node->right);

    // Return the sum of values of nodes in left and right subtrees and
    // old_value of this node
    return node->data + old_val;
}

// A utility function to print inorder traversal of a Binary Tree
void printInorder(struct node* node)
{
     if (node == NULL)
          return;
     printInorder(node->left);
     printf("%d ", node->data);
     printInorder(node->right);
}

/* Utility function to create a new Binary Tree node */
struct node* newNode(int data)
{
  struct node *temp = new struct node;
  temp->data = data;
  temp->left = NULL;
  temp->right = NULL;

  return temp;
}

/* Driver function to test above functions */
int main()
{
  struct node *root = NULL;
  int x;

  /* Constructing tree given in the above figure */
  root = newNode(10);
  root->left = newNode(-2);
  root->right = newNode(6);
  root->left->left = newNode(8);
  root->left->right = newNode(-4);
  root->right->left = newNode(7);
  root->right->right = newNode(5);

  toSumTree(root);

  // Print inorder traversal of the converted tree to test result of toSumTree()
  printf("Inorder Traversal of the resultant tree is: \n");
  printInorder(root);

  getchar();
  return 0;
}

Java

// Java program to convert a tree into its sum tree

// A binary tree node
class Node
{
    int data;
    Node left, right;

    Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class BinaryTree
{
    Node root;

    // Convert a given tree to a tree where every node contains sum of
    // values of nodes in left and right subtrees in the original tree
    int toSumTree(Node node)
    {
        // Base case
        if (node == null)
            return 0;

        // Store the old value
        int old_val = node.data;

        // Recursively call for left and right subtrees and store the sum
        // as new value of this node
        node.data = toSumTree(node.left) + toSumTree(node.right);

        // Return the sum of values of nodes in left and right subtrees
        // and old_value of this node
        return node.data + old_val;
    }

    // A utility function to print inorder traversal of a Binary Tree
    void printInorder(Node node)
    {
        if (node == null)
            return;
        printInorder(node.left);
        System.out.print(node.data + " ");
        printInorder(node.right);
    }

    /* Driver function to test above functions */
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();

        /* Constructing tree given in the above figure */
        tree.root = new Node(10);
        tree.root.left = new Node(-2);
        tree.root.right = new Node(6);
        tree.root.left.left = new Node(8);
        tree.root.left.right = new Node(-4);
        tree.root.right.left = new Node(7);
        tree.root.right.right = new Node(5);

        tree.toSumTree(tree.root);

        // Print inorder traversal of the converted tree to test result
        // of toSumTree()
        System.out.println("Inorder Traversal of the resultant tree is:");
        tree.printInorder(tree.root);
    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python3 program to convert a tree
# into its sum tree

# Node definition
class node:

    def __init__(self, data):
        self.left = None
        self.right = None
        self.data = data

# Convert a given tree to a tree where
# every node contains sum of values of
# nodes in left and right subtrees
# in the original tree
def toSumTree(Node) :

    # Base case
    if(Node == None) :
        return 0

    # Store the old value
    old_val = Node.data

    # Recursively call for left and
    # right subtrees and store the sum as
    # new value of this node
    Node.data = toSumTree(Node.left) + \
                toSumTree(Node.right)

    # Return the sum of values of nodes
    # in left and right subtrees and
    # old_value of this node
    return Node.data + old_val

# A utility function to print
# inorder traversal of a Binary Tree
def printInorder(Node) :
    if (Node == None) :
        return
    printInorder(Node.left)
    print(Node.data, end = " ")
    printInorder(Node.right)

# Utility function to create a new Binary Tree node
def newNode(data) :
    temp = node(0)
    temp.data = data
    temp.left = None
    temp.right = None

    return temp

# Driver Code
if __name__ == "__main__":
    root = None
    x = 0

    # Constructing tree given in the above figure
    root = newNode(10)
    root.left = newNode(-2)
    root.right = newNode(6)
    root.left.left = newNode(8)
    root.left.right = newNode(-4)
    root.right.left = newNode(7)
    root.right.right = newNode(5)

    toSumTree(root)

    # Print inorder traversal of the converted
    # tree to test result of toSumTree()
    print("Inorder Traversal of the resultant tree is: ")
    printInorder(root)

# This code is contributed by Arnab Kundu

C#

// C# program to convert a tree
// into its sum tree
using System;

// A binary tree node
public class Node
{
    public int data;
    public Node left, right;

    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class GFG
{
public Node root;

// Convert a given tree to a tree where
// every node contains sum of values of
// nodes in left and right subtrees in
// the original tree
public virtual int toSumTree(Node node)
{
    // Base case
    if (node == null)
    {
        return 0;
    }

    // Store the old value
    int old_val = node.data;

    // Recursively call for left and
    // right subtrees and store the sum
    // as new value of this node
    node.data = toSumTree(node.left) +
                toSumTree(node.right);

    // Return the sum of values of nodes
    // in left and right subtrees old_value
    // of this node
    return node.data + old_val;
}

// A utility function to print
// inorder traversal of a Binary Tree
public virtual void printInorder(Node node)
{
    if (node == null)
    {
        return;
    }
    printInorder(node.left);
    Console.Write(node.data + " ");
    printInorder(node.right);
}

// Driver Code
public static void Main(string[] args)
{
    GFG tree = new GFG();

    /* Constructing tree given in
       the above figure */
    tree.root = new Node(10);
    tree.root.left = new Node(-2);
    tree.root.right = new Node(6);
    tree.root.left.left = new Node(8);
    tree.root.left.right = new Node(-4);
    tree.root.right.left = new Node(7);
    tree.root.right.right = new Node(5);

    tree.toSumTree(tree.root);

    // Print inorder traversal of the
    // converted tree to test result of toSumTree()
    Console.WriteLine("Inorder Traversal of " +
                     "the resultant tree is:");
    tree.printInorder(tree.root);
}
}

// This code is contributed by Shrikant13

Javascript

<script>

// JavaScript program to convert a tree
// into its sum tree

// A binary tree node
class Node
{
    constructor(item)
    {
        this.data = item;
        this.left = null;
        this.right = null;
    }
}


var root = null;

// Convert a given tree to a tree where
// every node contains sum of values of
// nodes in left and right subtrees in
// the original tree
function toSumTree(node)
{
    // Base case
    if (node == null)
    {
        return 0;
    }

    // Store the old value
    var old_val = node.data;

    // Recursively call for left and
    // right subtrees and store the sum
    // as new value of this node
    node.data = toSumTree(node.left) +
                toSumTree(node.right);

    // Return the sum of values of nodes
    // in left and right subtrees old_value
    // of this node
    return node.data + old_val;
}

// A utility function to print
// inorder traversal of a Binary Tree
function printInorder(node)
{
    if (node == null)
    {
        return;
    }
    printInorder(node.left);
    document.write(node.data + " ");
    printInorder(node.right);
}

// Driver Code

/* Constructing tree given in
   the above figure */
root = new Node(10);
root.left = new Node(-2);
root.right = new Node(6);
root.left.left = new Node(8);
root.left.right = new Node(-4);
root.right.left = new Node(7);
root.right.right = new Node(5);
toSumTree(root);
// Print inorder traversal of the
// converted tree to test result of toSumTree()
document.write("Inorder Traversal of " +
                 "the resultant tree is:<br>");
printInorder(root);


</script>

Output

Inorder Traversal of the resultant tree is: 
 0 4 0 20 0 12 0

Time Complexity: The solution involves a simple traversal of the given tree. So the time complexity is O(n) where n is the number of nodes in the given Binary Tree.
Auxiliary Space : O(1) since using constant variables