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.
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 <iostream> #include <stdlib.h> #include <map> 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<int, int> &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<int, int> diagonalSum; diagonalSumUtil(root, 0, diagonalSum); map<int, int>::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<TreeNode> queue = new LinkedList<TreeNode>(); // Map to store sum of node's data lying diagonally Map<Integer, Integer> 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<Entry<Integer, Integer>> set = map.entrySet(); // Make an iterator Iterator<Entry<Integer, Integer>> 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<Integer, Integer> 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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