Difference between sums of odd level and even level nodes in an N-ary Tree
Given an N-ary Tree rooted at 1, the task is to find the difference between the sum of nodes at the odd level and the sum of nodes at even level.
Examples:
Input:
4
/ | \
2 3 -5
/ \ / \
-1 3 -2 6
Output: 10
Explanation:
Sum of nodes at even levels = 2 + 3 + (-5) = 0
Sum of nodes at odd levels = 4 + (-1) + 3 + (-2) + 6 = 10
Hence, the required difference is 10.Input:
1
/ | \
2 -1 3
/ \ \
4 5 8
/ / | \
2 6 12 7Output: -13
Approach: To solve the problem, the idea is to find the respective sums of the nodes at the even and odd levels using Level Order Traversal and calculate the difference between them. Follow the steps below to solve the problem:
- Initialize a Queue to store nodes and their respective levels.
- Initialize variables evenSum and oddSum to store the sum of nodes at the even and odd levels respectively.
- Push the root of the N-ary Tree along with its corresponding level, i.e., 1, into the Queue.
- Now, iterate and repeat the following steps until the Queue becomes empty:
- Pop the nodes from the Queue. Store the level of the popped node in a variable, say currentLevel.
- If currentLevel is even, add the value of the node to evenSum. Otherwise, add to oddSum.
- Push all its children to the Queue and set their respective levels as currentLevel + 1.
- Once the above steps are completed, calculate and print the difference between oddSum and evenSum.
Below is the implementation of the above approach:
C++
// C++ Program to implement // the above approach #include <bits/stdc++.h> using namespace std; // Structure of a node // of an n-ary tree struct Node { int val; vector<Node*> children; }; // Function to create a // new tree node Node* newNode( int val) { Node* temp = new Node; temp->val = val; return temp; } // Function to find the difference // between of sums node values of // odd and even levels in an N-ary tree int evenOddLevelDifference(Node* root) { // Store the sums of nodes at // even and odd levels int evenSum = 0, oddSum = 0; // Initialize a queue to store // pair of node and level queue<pair<Node*, int > > q; // Push the root into the // queue with level 1 q.push({ root, 1 }); // Iterate all levels // of tree are traversed while (!q.empty()) { // Store the node at the // front of the queue pair<Node*, int > currNode = q.front(); // Pop the front node q.pop(); // Store the current level int currLevel = currNode.second; // Store the current node value int currVal = currNode.first->val; // If current node // level is odd if (currLevel % 2) // Add to odd sum oddSum += currVal; else // Add to even sum evenSum += currVal; // Push all the children of current node // with increasing current level by 1 for ( auto child : currNode.first->children) { q.push({ child, currLevel + 1 }); } } // Return the difference return (oddSum - evenSum); } // Driver Code int main() { // Create the N-ary Tree Node* root = newNode(4); root->children.push_back(newNode(2)); root->children.push_back(newNode(3)); root->children.push_back(newNode(-5)); root->children[0]->children.push_back(newNode(-1)); root->children[0]->children.push_back(newNode(3)); root->children[2]->children.push_back(newNode(-2)); root->children[2]->children.push_back(newNode(6)); cout << evenOddLevelDifference(root); return 0; } |
Java
// Java program to implement // the above approach import java.util.ArrayList; import java.util.LinkedList; import java.util.Queue; class GFG{ // Structure of a node // of an n-ary tree static class Node { int val; ArrayList<Node> children; public Node( int val) { this .val = val; this .children = new ArrayList<Node>(); } }; static class Pair { Node first; int second; public Pair(Node node, int val) { this .first = node; this .second = val; } } // Function to find the difference // between of sums node values of // odd and even levels in an N-ary tree static int evenOddLevelDifference(Node root) { // Store the sums of nodes at // even and odd levels int evenSum = 0 , oddSum = 0 ; // Initialize a queue to store // pair of node and level Queue<Pair> q = new LinkedList<>(); // Push the root into the // queue with level 1 q.add( new Pair(root, 1 )); // Iterate all levels // of tree are traversed while (!q.isEmpty()) { // Store the node at the // front of the queue Pair currNode = q.poll(); // Store the current level int currLevel = currNode.second; // Store the current node value int currVal = currNode.first.val; // If current node // level is odd if (currLevel % 2 == 1 ) // Add to odd sum oddSum += currVal; else // Add to even sum evenSum += currVal; // Push all the children of current node // with increasing current level by 1 for (Node child : currNode.first.children) { q.add( new Pair(child, currLevel + 1 )); } } // Return the difference return (oddSum - evenSum); } // Driver Code public static void main(String[] args) { // Create the N-ary Tree Node root = new Node( 4 ); root.children.add( new Node( 2 )); root.children.add( new Node( 3 )); root.children.add( new Node(- 5 )); root.children.get( 0 ).children.add( new Node(- 1 )); root.children.get( 0 ).children.add( new Node( 3 )); root.children.get( 2 ).children.add( new Node(- 2 )); root.children.get( 2 ).children.add( new Node( 6 )); System.out.println(evenOddLevelDifference(root)); } } // This code is contributed by sanjeev2552 |
Python3
# Python3 program to implement # the above approach # Structure of a node # of an n-ary tree class Node: def __init__( self , val): self .val = val self .children = [] # Function to create a # new tree node def newNode(val): temp = Node(val) return temp # Function to find the difference # between of sums node values of # odd and even levels in an N-ary tree def evenOddLevelDifference(root): # Store the sums of nodes at # even and odd levels evenSum = 0 oddSum = 0 # Initialize a queue to store # pair of node and level q = [] # Push the root into the # queue with level 1 q.append([root, 1 ]) # Iterate all levels # of tree are traversed while ( len (q) ! = 0 ): # Store the node at the # front of the queue currNode = q[ 0 ] # Pop the front node q.pop( 0 ) # Store the current level currLevel = currNode[ 1 ] # Store the current node value currVal = currNode[ 0 ].val # If current node # level is odd if (currLevel % 2 ! = 0 ): # Add to odd sum oddSum + = currVal else : # Add to even sum evenSum + = currVal # Push all the children of current node # with increasing current level by 1 for child in currNode[ 0 ].children: q.append([child, currLevel + 1 ]) # Return the difference return (oddSum - evenSum) # Driver code if __name__ = = "__main__" : # Create the N-ary Tree root = newNode( 4 ) root.children.append(newNode( 2 )) root.children.append(newNode( 3 )) root.children.append(newNode( - 5 )) root.children[ 0 ].children.append(newNode( - 1 )) root.children[ 0 ].children.append(newNode( 3 )) root.children[ 2 ].children.append(newNode( - 2 )) root.children[ 2 ].children.append(newNode( 6 )) print (evenOddLevelDifference(root)) # This code is contributed by rutvik_56 |
C#
// C# program to implement // the above approach using System; using System.Collections; using System.Collections.Generic; class GFG{ // Structure of a node // of an n-ary tree class Node { public int val; public ArrayList children; public Node( int val) { this .val = val; this .children = new ArrayList(); } }; class Pair { public Node first; public int second; public Pair(Node node, int val) { this .first = node; this .second = val; } } // Function to find the difference // between of sums node values of // odd and even levels in an N-ary tree static int evenOddLevelDifference(Node root) { // Store the sums of nodes at // even and odd levels int evenSum = 0, oddSum = 0; // Initialize a queue to store // pair of node and level Queue q = new Queue(); // Push the root into the // queue with level 1 q.Enqueue( new Pair(root, 1)); // Iterate all levels // of tree are traversed while (q.Count != 0) { // Store the node at the // front of the queue Pair currNode = (Pair)q.Dequeue(); // Store the current level int currLevel = currNode.second; // Store the current node value int currVal = currNode.first.val; // If current node // level is odd if (currLevel % 2 == 1) // Add to odd sum oddSum += currVal; else // Add to even sum evenSum += currVal; // Push all the children of current node // with increasing current level by 1 foreach (Node child in currNode.first.children) { q.Enqueue( new Pair(child, currLevel + 1)); } } // Return the difference return (oddSum - evenSum); } // Driver Code public static void Main( string [] args) { // Create the N-ary Tree Node root = new Node(4); root.children.Add( new Node(2)); root.children.Add( new Node(3)); root.children.Add( new Node(-5)); ((Node)root.children[0]).children.Add( new Node(-1)); ((Node)root.children[0]).children.Add( new Node(3)); ((Node)root.children[2]).children.Add( new Node(-2)); ((Node)root.children[2]).children.Add( new Node(6)); Console.Write(evenOddLevelDifference(root)); } } // This code is contributed by pratham76 |
Javascript
<script> // JavaScript implementation of the above approach // Structure of a node of an n-ary tree // Structure of a Tree Node class Node { constructor(val) { this .children = []; this .val = val; } } // Function to find the difference // between of sums node values of // odd and even levels in an N-ary tree function evenOddLevelDifference(root) { // Store the sums of nodes at // even and odd levels let evenSum = 0, oddSum = 0; // Initialize a queue to store // pair of node and level let q = []; // Push the root into the // queue with level 1 q.push([root, 1]); // Iterate all levels // of tree are traversed while (q.length != 0) { // Store the node at the // front of the queue let currNode = q[0]; q.shift(); // Store the current level let currLevel = currNode[1]; // Store the current node value let currVal = currNode[0].val; // If current node // level is odd if (currLevel % 2 == 1) // Add to odd sum oddSum += currVal; else // Add to even sum evenSum += currVal; // Push all the children of current node // with increasing current level by 1 for (let child = 0; child < (currNode[0].children).length; child++) { q.push([currNode[0].children[child], currLevel + 1]); } } // Return the difference return (oddSum - evenSum); } // Create the N-ary Tree let root = new Node(4); root.children.push( new Node(2)); root.children.push( new Node(3)); root.children.push( new Node(-5)); (root.children[0]).children.push( new Node(-1)); (root.children[0]).children.push( new Node(3)); (root.children[2]).children.push( new Node(-2)); (root.children[2]).children.push( new Node(6)); document.write(evenOddLevelDifference(root)); </script> |
10
Time Complexity: O(N)
Auxiliary Space: O(N)
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