Diagonal Traversal of Binary Tree
Consider lines of slope -1 passing between nodes. Given a Binary Tree, print all diagonal elements in a binary tree belonging to the same line.
Input : Root of below tree
Output : Diagonal Traversal of binary tree : 8 10 14 3 6 7 13 1 4
The idea is to use a map. We use different slope distances and use them as key in the map. Value in the map is a vector (or dynamic array) of nodes. We traverse the tree to store values in the map. Once map is built, we print the contents of it.
Below is the implementation of the above idea.
C++
// C++ program for diagnoal // traversal of Binary Tree#include <bits/stdc++.h>using namespace std;// Tree nodestruct Node{ int data; Node *left, *right;};/* root - root of the binary tree d - distance of current line from rightmost -topmost slope. diagonalPrint - multimap to store Diagonal elements (Passed by Reference) */void diagonalPrintUtil(Node* root, int d, map<int, vector<int>> &diagonalPrint){ // Base case if (!root) return; // Store all nodes of same // line together as a vector diagonalPrint[d].push_back(root->data); // Increase the vertical // distance if left child diagonalPrintUtil(root->left, d + 1, diagonalPrint); // Vertical distance remains // same for right child diagonalPrintUtil(root->right, d, diagonalPrint);}// Print diagonal traversal // of given binary treevoid diagonalPrint(Node* root){ // create a map of vectors // to store Diagonal elements map<int, vector<int> > diagonalPrint; diagonalPrintUtil(root, 0, diagonalPrint); cout << "Diagonal Traversal of binary tree : \n"; for (auto it :diagonalPrint) { vector<int> v=it.second; for(auto it:v) cout<<it<<" "; cout<<endl; }}// Utility method to create a new nodeNode* newNode(int data){ Node* node = new Node; node->data = data; node->left = node->right = NULL; return node;}// Driver programint main(){ Node* root = newNode(8); root->left = newNode(3); root->right = newNode(10); root->left->left = newNode(1); root->left->right = newNode(6); root->right->right = newNode(14); root->right->right->left = newNode(13); root->left->right->left = newNode(4); root->left->right->right = newNode(7); /* 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);*/ diagonalPrint(root); return 0;} |
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Java
// Java program for diagonal // traversal of Binary Treeimport java.util.HashMap;import java.util.Map.Entry;import java.util.Vector;public class DiagonalTraversalBTree { // Tree node static class Node { int data; Node left; Node right; //constructor Node(int data) { this.data=data; left = null; right =null; } } /* root - root of the binary tree d - distance of current line from rightmost -topmost slope. diagonalPrint - HashMap to store Diagonal elements (Passed by Reference) */ static void diagonalPrintUtil(Node root,int d, HashMap<Integer,Vector<Integer>> diagonalPrint) { // Base case if (root == null) return; // get the list at the particular d value Vector<Integer> k = diagonalPrint.get(d); // k is null then create a // vector and store the data if (k == null) { k = new Vector<>(); k.add(root.data); } // k is not null then update the list else { k.add(root.data); } // Store all nodes of same line // together as a vector diagonalPrint.put(d,k); // Increase the vertical distance // if left child diagonalPrintUtil(root.left, d + 1, diagonalPrint); // Vertical distance remains // same for right child diagonalPrintUtil(root.right, d, diagonalPrint); } // Print diagonal traversal // of given binary tree static void diagonalPrint(Node root) { // create a map of vectors // to store Diagonal elements HashMap<Integer,Vector<Integer>> diagonalPrint = new HashMap<>(); diagonalPrintUtil(root, 0, diagonalPrint); System.out.println("Diagonal Traversal of Binnary Tree"); for (Entry<Integer, Vector<Integer>> entry : diagonalPrint.entrySet()) { System.out.println(entry.getValue()); } } // Driver program public static void main(String[] args) { Node root = new Node(8); root.left = new Node(3); root.right = new Node(10); root.left.left = new Node(1); root.left.right = new Node(6); root.right.right = new Node(14); root.right.right.left = new Node(13); root.left.right.left = new Node(4); root.left.right.right = new Node(7); diagonalPrint(root); }}// This code is contributed by Sumit Ghosh |
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Python
# Python program for diagonal # traversal of Binary Tree# A binary tree nodeclass Node: # Constructor to create a # new binary tree node def __init__(self, data): self.data = data self.left = None self.right = None""" root - root of the binary tree d - distance of current line from rightmost -topmost slope. diagonalPrint - multimap to store Diagonal elements (Passed by Reference) """def diagonalPrintUtil(root, d, diagonalPrintMap): # Base Case if root is None: return # Store all nodes of same line # together as a vector try : diagonalPrintMap[d].append(root.data) except KeyError: diagonalPrintMap[d] = [root.data] # Increase the vertical distance # if left child diagonalPrintUtil(root.left, d+1, diagonalPrintMap) # Vertical distance remains # same for right child diagonalPrintUtil(root.right, d, diagonalPrintMap)# Print diagonal traversal of given binary treedef diagonalPrint(root): # Create a dict to store diagnoal elements diagonalPrintMap = dict() # Find the diagonal traversal diagonalPrintUtil(root, 0, diagonalPrintMap) print "Diagonal Traversal of binary tree : " for i in diagonalPrintMap: for j in diagonalPrintMap[i]: print j, print ""# Driver Program root = Node(8)root.left = Node(3)root.right = Node(10)root.left.left = Node(1)root.left.right = Node(6)root.right.right = Node(14)root.right.right.left = Node(13)root.left.right.left = Node(4)root.left.right.right = Node(7)diagonalPrint(root)# This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
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Output :
Diagonal Traversal of binary tree : 8 10 14 3 6 7 13 1 4
This article is contributed by Aditya Goel. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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