Diagonal Sum of a Binary Tree

Consider lines of slope -1 passing between nodes (dotted lines in below diagram). Diagonal sum in a binary tree is sum of all node’s data lying between these lines. Given a Binary Tree, print all diagonal sums.

For the following input tree, output should be 9, 19, 42.
9 is sum of 1, 3 and 5.
19 is sum of 2, 6, 4 and 7.
42 is sum of 9, 10, 11 and 12. Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Algorithm:
The idea is to keep track of vertical distance from top diagonal passing through root. We increment the vertical distance we go down to next diagonal.
1. Add root with vertical distance as 0 to the queue.
2. Process the sum of all right child and right of right child and so on.
3. Add left child current node into the queue for later processing. The vertical distance of left child is vertical distance of current node plus 1.
4. Keep doing 2nd, 3rd and 4th step till the queue is empty.

Following is the implementation of above idea.

C++

 // C++ Program to find diagonal // sum in a Binary Tree #include #include #include using namespace std;    struct Node {     int data;     struct Node* left;     struct Node* right; };    struct Node* newNode(int data) {     struct Node* Node =             (struct Node*)malloc(sizeof(struct Node));            Node->data = data;     Node->left = Node->right = NULL;        return Node; }    // root - root of the binary tree // vd - vertical distance diagonally // diagonalSum - map to store Diagonal  // Sum(Passed by Reference) void diagonalSumUtil(struct Node* root,                 int vd, map &diagonalSum) {     if(!root)         return;                diagonalSum[vd] += root->data;        // increase the vertical distance if left child     diagonalSumUtil(root->left, vd + 1, diagonalSum);        // vertical distance remains same for right child     diagonalSumUtil(root->right, vd, diagonalSum); }    // Function to calculate diagonal  // sum of given binary tree void diagonalSum(struct Node* root) {        // create a map to store Diagonal Sum     map diagonalSum;             diagonalSumUtil(root, 0, diagonalSum);        map::iterator it;         cout << "Diagonal sum in a binary tree is - ";            for(it = diagonalSum.begin();                 it != diagonalSum.end(); ++it)     {         cout << it->second << " ";     } }    // Driver code int main() {     struct Node* root = newNode(1);     root->left = newNode(2);     root->right = newNode(3);     root->left->left = newNode(9);     root->left->right = newNode(6);     root->right->left = newNode(4);     root->right->right = newNode(5);     root->right->left->right = newNode(7);     root->right->left->left = newNode(12);     root->left->right->left = newNode(11);     root->left->left->right = newNode(10);        diagonalSum(root);        return 0; }    // This code is contributed by Aditya Goel

Java

 // Java Program to find diagonal sum in a Binary Tree import java.util.*; import java.util.Map.Entry;    //Tree node class TreeNode {     int data; //node data     int vd; //vertical distance diagonally     TreeNode left, right; //left and right child's reference        // Tree node constructor     public TreeNode(int data)     {         this.data = data;         vd = Integer.MAX_VALUE;         left = right = null;     } }    // Tree class class Tree {     TreeNode root;//Tree root        // Tree constructor     public Tree(TreeNode root)  {  this.root = root;  }        // Diagonal sum method     public void diagonalSum()     {         // Queue which stores tree nodes         Queue queue = new LinkedList();            // Map to store sum of node's data lying diagonally         Map map = new TreeMap<>();            // Assign the root's vertical distance as 0.         root.vd = 0;            // Add root node to the queue         queue.add(root);            // Loop while the queue is not empty         while (!queue.isEmpty())         {             // Remove the front tree node from queue.             TreeNode curr = queue.remove();                // Get the vertical distance of the dequeued node.             int vd = curr.vd;                // Sum over this node's right-child, right-of-right-child             // and so on             while (curr != null)             {                 int prevSum = (map.get(vd) == null)? 0: map.get(vd);                 map.put(vd, prevSum + curr.data);                    // If for any node the left child is not null add                 // it to the queue for future processing.                 if (curr.left != null)                 {                     curr.left.vd = vd+1;                     queue.add(curr.left);                 }                    // Move to the current node's right child.                 curr = curr.right;             }         }            // Make an entry set from map.         Set> set = map.entrySet();            // Make an iterator         Iterator> iterator = set.iterator();            // Traverse the map elements using the iterator.          System.out.print("Diagonal sum in a binary tree is - ");         while (iterator.hasNext())         {             Map.Entry me = iterator.next();                System.out.print(me.getValue()+" ");         }     } }    //Driver class public class DiagonalSum {     public static void main(String[] args)     {         TreeNode root = new TreeNode(1);         root.left = new TreeNode(2);         root.right = new TreeNode(3);         root.left.left = new TreeNode(9);         root.left.right = new TreeNode(6);         root.right.left = new TreeNode(4);         root.right.right = new TreeNode(5);         root.right.left.left = new TreeNode(12);         root.right.left.right = new TreeNode(7);         root.left.right.left = new TreeNode(11);         root.left.left.right = new TreeNode(10);         Tree tree = new Tree(root);         tree.diagonalSum();     } }

Python3

 # Program to find diagonal sum in a Binary Tree    class newNode:      def __init__(self, data):          self.data = data          self.left = self.right = None            # Function to compute height and  # root - root of the binary tree  # vd - vertical distance diagonally  # diagonalSum - map to store Diagonal  # Sum(Passed by Reference)  def diagonalSumUtil(root, vd, diagonalSum) :        if(not root):          return                if vd not in diagonalSum:         diagonalSum[vd] = 0     diagonalSum[vd] += root.data         # increase the vertical distance     # if left child      diagonalSumUtil(root.left, vd + 1,                            diagonalSum)         # vertical distance remains same      # for right child      diagonalSumUtil(root.right, vd,                        diagonalSum)     # Function to calculate diagonal  # sum of given binary tree  def diagonalSum(root) :        # create a map to store Diagonal Sum      diagonalSum = dict()             diagonalSumUtil(root, 0, diagonalSum)         print("Diagonal sum in a binary tree is - ",                                         end = "")            for it in diagonalSum:         print(diagonalSum[it], end = " ")            # Driver Code  if __name__ == '__main__':     root = newNode(1)      root.left = newNode(2)      root.right = newNode(3)      root.left.left = newNode(9)      root.left.right = newNode(6)      root.right.left = newNode(4)      root.right.right = newNode(5)      root.right.left.right = newNode(7)      root.right.left.left = newNode(12)      root.left.right.left = newNode(11)      root.left.left.right = newNode(10)         diagonalSum(root)    # This code is contributed  # by SHUBHAMSINGH10

Output:

Diagonal sum in a binary tree is - 9 19 42

Exercise:
This problem was for diagonals from top to bottom and slope -1. Try the same problem for slope +1.

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Improved By : SHUBHAMSINGH10

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