Change a Binary Tree so that every node stores sum of all nodes in left subtree

Given a Binary Tree, change the value in each node to sum of all the values in the nodes in the left subtree including its own.

Examples:

Input : 
     1
   /   \
 2      3

Output :
    3
  /   \
 2     3


Input
       1
      / \
     2   3
    / \   \
   4   5   6
Output:
      12
     / \
    6   3
   / \   \
  4   5   6

We strongly recommend you to minimize your browser and try this yourself first.
The idea is to traverse the given tree in bottom up manner. For every node, recursively compute sum of nodes in left and right subtrees. Add sum of nodes in left subtree to current node and return sum of nodes under current subtree.

Below is the implementation of above idea. 

C++

// C++ program to store sum of nodes
// in left subtree in every node
#include<bits/stdc++.h>

using namespace std;

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

    /* Constructor that allocates a new node with the
    given data and NULL left and right pointers. */
    node(int data)
    {
        this->data = data;
        this->left = NULL;
        this->right = NULL;
    }
};

// Function to modify a Binary Tree
// so that every node stores sum of
// values in its left child including
// its own value
int updatetree(node *root)
{
    // Base cases
    if (!root)
        return 0;
    if (root->left == NULL && root->right == NULL)
        return root->data;

    // Update left and right subtrees
    int leftsum = updatetree(root->left);
    int rightsum = updatetree(root->right);

    // Add leftsum to current node
    root->data += leftsum;

    // Return sum of values under root
    return root->data + rightsum;
}

// Utility function to do inorder traversal
void inorder(node* node)
{
    if (node == NULL)
        return;
    inorder(node->left);
    cout<<node->data<<" ";
    inorder(node->right);
}

// Driver code
int main()
{
    /* Let us construct below tree
                1
            / \
            2 3
            / \ \
            4 5 6 */
    struct node *root = new node(1);
    root->left     = new node(2);
    root->right = new node(3);
    root->left->left = new node(4);
    root->left->right = new node(5);
    root->right->right = new node(6);

    updatetree(root);

    cout << "Inorder traversal of the modified tree is: \n";
    inorder(root);
    return 0;
}

// This code is contributed by rathbhupendra

C

// C program to store  sum of nodes in left subtree in every
// node
#include<bits/stdc++.h>
using namespace std;

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

// Function to modify a Binary Tree so that every node
// stores sum of values in its left child including its
// own value
int updatetree(node *root)
{
    // Base cases
    if (!root)
        return 0;
    if (root->left == NULL && root->right == NULL)
        return root->data;

    // Update left and right subtrees
    int leftsum  = updatetree(root->left);
    int rightsum = updatetree(root->right);

    // Add leftsum to current node
    root->data += leftsum;

    // Return sum of values under root
    return root->data + rightsum;
}

// Utility function to do inorder traversal
void inorder(struct node* node)
{
    if (node == NULL)
        return;
    inorder(node->left);
    printf("%d ", node->data);
    inorder(node->right);
}

// Utility function to create a new node
struct node* newNode(int data)
{
    struct node* node =
        (struct node*)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return(node);
}

// Driver program
int main()
{
    /* Let us construct below tree
                1
               / \
              2   3
             / \   \
            4   5   6    */
    struct node *root  = newNode(1);
    root->left         = newNode(2);
    root->right        = newNode(3);
    root->left->left   = newNode(4);
    root->left->right  = newNode(5);
    root->right->right = newNode(6);

    updatetree(root);

    cout << "Inorder traversal of the modified tree is \n";
    inorder(root);
    return 0;
}

Java

// Java program to store sum of nodes in left subtree in every
// node
class GfG {

// A tree node
static class node
{
    int data;
    node left, right;
}

// Function to modify a Binary Tree so that every node
// stores sum of values in its left child including its
// own value
static int updatetree(node root)
{
    // Base cases
    if (root == null)
        return 0;
    if (root.left == null && root.right == null)
        return root.data;

    // Update left and right subtrees
    int leftsum = updatetree(root.left);
    int rightsum = updatetree(root.right);

    // Add leftsum to current node
    root.data += leftsum;

    // Return sum of values under root
    return root.data + rightsum;
}

// Utility function to do inorder traversal
static void inorder(node node)
{
    if (node == null)
        return;
    inorder(node.left);
    System.out.print(node.data + " ");
    inorder(node.right);
}

// Utility function to create a new node
static node newNode(int data)
{
    node node = new node();
    node.data = data;
    node.left = null;
    node.right = null;
    return(node);
}

// Driver program
public static void main(String[] args)
{
    /* Let us construct below tree
                1
            / \
            2 3
            / \ \
            4 5 6 */
    node root = newNode(1);
    root.left         = newNode(2);
    root.right     = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.right = newNode(6);

    updatetree(root);


    System.out.println("Inorder traversal of the modified tree is");
    inorder(root);
}
}

Python3

# Python3 program to store sum of nodes
# in left subtree in every node

# Binary Tree Node

# utility that allocates a new Node
# with the given key
class newNode:

    # Construct to create a new node
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None

# Function to modify a Binary Tree so
# that every node stores sum of values
# in its left child including its own value
def updatetree(root):

    # Base cases
    if (not root):
        return 0
    if (root.left == None and
        root.right == None) :
        return root.data

    # Update left and right subtrees
    leftsum = updatetree(root.left)
    rightsum = updatetree(root.right)

    # Add leftsum to current node
    root.data += leftsum

    # Return sum of values under root
    return root.data + rightsum

# Utility function to do inorder traversal
def inorder(node) :

    if (node == None) :
        return
    inorder(node.left)
    print(node.data, end = " ")
    inorder(node.right)

# Driver Code
if __name__ == '__main__':

    """ Let us construct below tree
                    1
                / \
                2 3
                / \ \
                4 5 6 """
    root = newNode(1)
    root.left = newNode(2)
    root.right = newNode(3)
    root.left.left = newNode(4)
    root.left.right = newNode(5)
    root.right.right = newNode(6)

    updatetree(root)

    print("Inorder traversal of the modified tree is")
    inorder(root)

# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

C#

// C# program to store sum of nodes in left
// subtree in every node
using System;

class GfG
{

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

// Function to modify a Binary Tree so
// that every node stores sum of values
// in its left child including its own value
static int updatetree(node root)
{
    // Base cases
    if (root == null)
        return 0;
    if (root.left == null && root.right == null)
        return root.data;

    // Update left and right subtrees
    int leftsum = updatetree(root.left);
    int rightsum = updatetree(root.right);

    // Add leftsum to current node
    root.data += leftsum;

    // Return sum of values under root
    return root.data + rightsum;
}

// Utility function to do inorder traversal
static void inorder(node node)
{
    if (node == null)
        return;
    inorder(node.left);
    Console.Write(node.data + " ");
    inorder(node.right);
}

// Utility function to create a new node
static node newNode(int data)
{
    node node = new node();
    node.data = data;
    node.left = null;
    node.right = null;
    return(node);
}

// Driver code
public static void Main()
{
    /* Let us construct below tree
                1
            / \
            2 3
            / \ \
            4 5 6 */
    node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.right = newNode(6);

    updatetree(root);

    Console.WriteLine("Inorder traversal of the modified tree is");
    inorder(root);
}
}

/* This code is contributed by Rajput-Ji*/

Javascript

<script>

// Javascript program to store sum of nodes in left
// subtree in every node

// A tree node
class node
{
  constructor()
  {
    this.data = 0;
    this.left = null;
    this.right = null;
  }
}

// Function to modify a Binary Tree so
// that every node stores sum of values
// in its left child including its own value
function updatetree(root)
{
    // Base cases
    if (root == null)
        return 0;
    if (root.left == null && root.right == null)
        return root.data;

    // Update left and right subtrees
    var leftsum = updatetree(root.left);
    var rightsum = updatetree(root.right);

    // Add leftsum to current node
    root.data += leftsum;

    // Return sum of values under root
    return root.data + rightsum;
}

// Utility function to do inorder traversal
function inorder(node)
{
    if (node == null)
        return;
    inorder(node.left);
    document.write(node.data + " ");
    inorder(node.right);
}

// Utility function to create a new node
function newNode(data)
{
    var nod = new node();
    nod.data = data;
    nod.left = null;
    nod.right = null;
    return(nod);
}

// Driver code
/* Let us construct below tree
            1
        / \
        2 3
        / \ \
        4 5 6 */
var root = newNode(1);
root.left = newNode(2);
root.right = newNode(3);
root.left.left = newNode(4);
root.left.right = newNode(5);
root.right.right = newNode(6);
updatetree(root);
document.write("Inorder traversal of the modified tree is<br>");
inorder(root);

// This code is contributed by rrrtnx.
</script>

Output

Inorder traversal of the modified tree is: 
4 6 5 12 3 6 

Time Complexity: O(n)

Auxiliary space: O(n) for implicit call stack as using recursion

Thanks to Gaurav Ahrirwar for suggesting this solution.