Sum of all the numbers that are formed from root to leaf paths

• Difficulty Level : Medium
• Last Updated : 18 Jan, 2022

Given a binary tree, where every node value is a Digit from 1-9 .Find the sum of all the numbers which are formed from root to leaf paths.
For example consider the following Binary Tree.

6
/      \
3          5
/   \          \
2     5          4
/   \
7     4
There are 4 leaves, hence 4 root to leaf paths:
Path                    Number
6->3->2                   632
6->3->5->7               6357
6->3->5->4               6354
6->5>4                    654
Answer = 632 + 6357 + 6354 + 654 = 13997

The idea is to do a preorder traversal of the tree. In the preorder traversal, keep track of the value calculated till the current node, let this value be val. For every node, we update the val as val*10 plus node’s data.

C++

 // C++ program to find sum of// all paths from root to leaves#include using namespace std; class node{    public:    int data;    node *left, *right;}; // function to allocate new node with given datanode* newNode(int data){    node* Node = new node();    Node->data = data;    Node->left = Node->right = NULL;    return (Node);} // Returns sum of all root to leaf paths.// The first parameter is root// of current subtree, the second// parameter is value of the number formed// by nodes from root to this nodeint treePathsSumUtil(node *root, int val){    // Base case    if (root == NULL) return 0;     // Update val    val = (val*10 + root->data);     // if current node is leaf, return the current value of val    if (root->left==NULL && root->right==NULL)    return val;     // recur sum of values for left and right subtree    return treePathsSumUtil(root->left, val) +        treePathsSumUtil(root->right, val);} // A wrapper function over treePathsSumUtil()int treePathsSum(node *root){    // Pass the initial value as 0    // as there is nothing above root    return treePathsSumUtil(root, 0);} // Driver codeint main(){    node *root = newNode(6);    root->left = newNode(3);    root->right = newNode(5);    root->left->left = newNode(2);    root->left->right = newNode(5);    root->right->right = newNode(4);    root->left->right->left = newNode(7);    root->left->right->right = newNode(4);    cout<<"Sum of all paths is "<

C

 // C program to find sum of all paths from root to leaves#include #include  struct node{    int data;    struct node *left, *right;}; // function to allocate new node with given datastruct node* newNode(int data){    struct node* node = (struct node*)malloc(sizeof(struct node));    node->data = data;    node->left = node->right = NULL;    return (node);} // Returns sum of all root to leaf paths. The first parameter is root// of current subtree, the second parameter is value of the number formed// by nodes from root to this nodeint treePathsSumUtil(struct node *root, int val){    // Base case    if (root == NULL)  return 0;     // Update val    val = (val*10 + root->data);     // if current node is leaf, return the current value of val    if (root->left==NULL && root->right==NULL)       return val;     // recur sum of values for left and right subtree    return treePathsSumUtil(root->left, val) +           treePathsSumUtil(root->right, val);} // A wrapper function over treePathsSumUtil()int treePathsSum(struct node *root){    // Pass the initial value as 0 as there is nothing above root    return treePathsSumUtil(root, 0);} // Driver function to test the above functionsint main(){    struct node *root = newNode(6);    root->left        = newNode(3);    root->right       = newNode(5);    root->left->left  = newNode(2);    root->left->right = newNode(5);    root->right->right = newNode(4);    root->left->right->left = newNode(7);    root->left->right->right = newNode(4);    printf("Sum of all paths is %d", treePathsSum(root));    return 0;}

Java

 // Java program to find sum of all numbers that are formed from root// to leaf paths  // A binary tree nodeclass Node{    int data;    Node left, right;          Node(int item)    {        data = item;        left = right = null;    }}  class BinaryTree{    Node root;      // Returns sum of all root to leaf paths. The first parameter is    // root of current subtree, the second parameter is value of the     // number formed by nodes from root to this node    int treePathsSumUtil(Node node, int val)    {        // Base case        if (node == null)            return 0;          // Update val        val = (val * 10 + node.data);          // if current node is leaf, return the current value of val        if (node.left == null && node.right == null)            return val;          // recur sum of values for left and right subtree        return treePathsSumUtil(node.left, val)                + treePathsSumUtil(node.right, val);    }      // A wrapper function over treePathsSumUtil()    int treePathsSum(Node node)    {        // Pass the initial value as 0 as there is nothing above root        return treePathsSumUtil(node, 0);    }      // Driver program to test above functions    public static void main(String args[])    {        BinaryTree tree = new BinaryTree();        tree.root = new Node(6);        tree.root.left = new Node(3);        tree.root.right = new Node(5);        tree.root.right.right = new Node(4);        tree.root.left.left = new Node(2);        tree.root.left.right = new Node(5);        tree.root.left.right.right = new Node(4);        tree.root.left.right.left = new Node(7);                  System.out.print("Sum of all paths is " +                                 tree.treePathsSum(tree.root));      }   }  // This code has been contributed by Mayank Jaiswal

Python3

 # Python program to find sum of all paths from root to leaves # A Binary tree nodeclass Node:     # Constructor to create a new node    def __init__(self, data):        self.data = data        self.left = None        self.right = None # Returs sums of all root to leaf paths. The first parameter is root# of current subtree, the second paramete"r is value of the number# formed by nodes from root to this nodedef treePathsSumUtil(root, val):     # Base Case    if root is None:        return 0     # Update val    val = (val*10 + root.data)     # If current node is leaf, return the current value of val    if root.left is None and root.right is None:        return val     # Recur sum of values for left and right subtree    return (treePathsSumUtil(root.left, val) +            treePathsSumUtil(root.right, val)) # A wrapper function over treePathSumUtil()def treePathsSum(root):         # Pass the initial value as 0 as ther is nothing above root    return treePathsSumUtil(root, 0) # Driver function to test above functionroot = Node(6)root.left = Node(3)root.right = Node(5)root.left.left = Node(2)root.left.right = Node(5)root.right.right = Node(4)root.left.right.left = Node(7)root.left.right.right = Node(4)print ("Sum of all paths is", treePathsSum(root)) # This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

 // c# program to find sum of all numbers// that are formed from root to leaf pathsusing System; // A binary tree nodepublic class Node{    public int data;    public Node left, right;     public Node(int item)    {        data = item;        left = right = null;    }} class GFG{public Node root; // Returns sum of all root to leaf paths.// The first parameter is root of current// subtree, the second parameter is value// of the number formed by nodes from root// to this nodepublic virtual int treePathsSumUtil(Node node,                                    int val){    // Base case    if (node == null)    {        return 0;    }     // Update val    val = (val * 10 + node.data);     // if current node is leaf, return    // the current value of val    if (node.left == null && node.right == null)    {        return val;    }     // recur sum of values for left and right subtree    return treePathsSumUtil(node.left, val) +           treePathsSumUtil(node.right, val);} // A wrapper function over treePathsSumUtil()public virtual int treePathsSum(Node node){    // Pass the initial value as 0 as    // there is nothing above root    return treePathsSumUtil(node, 0);} // Driver Codepublic static void Main(string[] args){    GFG tree = new GFG();    tree.root = new Node(6);    tree.root.left = new Node(3);    tree.root.right = new Node(5);    tree.root.right.right = new Node(4);    tree.root.left.left = new Node(2);    tree.root.left.right = new Node(5);    tree.root.left.right.right = new Node(4);    tree.root.left.right.left = new Node(7);     Console.Write("Sum of all paths is " +                   tree.treePathsSum(tree.root));}} // This code is contributed by Shrikant13

Output:

Sum of all paths is 13997

Time Complexity: The above code is a simple preorder traversal code which visits every exactly once. Therefore, the time complexity is O(n) where n is the number of nodes in the given binary tree.