Count the nodes in the given Tree whose weight is a Perfect Number

Given a tree, and the weights of all the nodes, the task is to count the number of nodes whose weight is a Perfect number.

A perfect number is a positive integer that is equal to the sum of its proper divisors.

Examples:

Input:

Output: 0
Explanation:
There is no node with a weight that is a perfect number.

Approach:
In order to solve this problem, we perform Depth First Search(DFS) Traversal on the tree and for every node, check if its weight is a Perfect Number or not. We keep on incrementing the counter every time such a weight is obtained. The final value of that counter after the completion of the entire tree traversal is the answer.



Below is the implementation of the above approach:

C++

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// C++ implementation to Count the nodes in the
// given tree whose weight is a Perfect Number
  
#include <bits/stdc++.h>
using namespace std;
  
int ans = 0;
vector<int> graph[100];
vector<int> weight(100);
  
// Function that returns true if n is perfect
bool isPerfect(long long int n)
{
    // Variable to store sum of divisors
    long long int sum = 1;
  
    // Find all divisors and add them
    for (long long int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            if (i * i != n)
                sum = sum + i + n / i;
            else
                sum = sum + i;
        }
    }
  
    // Check if sum of divisors is equal to
    // n, then n is a perfect number
    if (sum == n && n != 1)
        return true;
  
    return false;
}
  
// Function to perform dfs
void dfs(int node, int parent)
{
  
    // If weight of the current node
    // is a perfect number
    if (isPerfect(weight[node]))
        ans += 1;
  
    for (int to : graph[node]) {
        if (to == parent)
            continue;
        dfs(to, node);
    }
}
  
// Driver code
int main()
{
  
    // Weights of the node
    weight[1] = 5;
    weight[2] = 10;
    weight[3] = 11;
    weight[4] = 8;
    weight[5] = 6;
  
    // Edges of the tree
    graph[1].push_back(2);
    graph[2].push_back(3);
    graph[2].push_back(4);
    graph[1].push_back(5);
  
    dfs(1, 1);
    cout << ans;
  
    return 0;
}

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Java

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// Java implementation to Count the nodes in the
// given tree whose weight is a Perfect Number
  
import java.util.*;
  
class GFG{
  
static int ans = 0;
static Vector<Integer> []graph = new Vector[100];
static int []weight = new int[100];
  
// Function that returns true if n is perfect
static boolean isPerfect(int n)
{
    // Variable to store sum of divisors
    int sum = 1;
  
    // Find all divisors and add them
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            if (i * i != n)
                sum = sum + i + n / i;
            else
                sum = sum + i;
        }
    }
  
    // Check if sum of divisors is equal to
    // n, then n is a perfect number
    if (sum == n && n != 1)
        return true;
  
    return false;
}
  
// Function to perform dfs
static void dfs(int node, int parent)
{
  
    // If weight of the current node
    // is a perfect number
    if (isPerfect(weight[node]))
        ans += 1;
  
    for (int to : graph[node]) {
        if (to == parent)
            continue;
        dfs(to, node);
    }
}
  
// Driver code
public static void main(String[] args)
{
  
    for (int i = 0; i < graph.length; i++)
        graph[i] = new Vector<Integer>();
          
    // Weights of the node
    weight[1] = 5;
    weight[2] = 10;
    weight[3] = 11;
    weight[4] = 8;
    weight[5] = 6;
  
    // Edges of the tree
    graph[1].add(2);
    graph[2].add(3);
    graph[2].add(4);
    graph[1].add(5);
  
    dfs(1, 1);
    System.out.print(ans);
  
}
}
  
// This code contributed by Princi Singh

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C#

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// C# implementation to count the 
// nodes in the given tree whose 
// weight is a Perfect Number
using System;
using System.Collections.Generic;
  
class GFG{
  
static int ans = 0;
static List<int> []graph = new List<int>[100];
static int []weight = new int[100];
  
// Function that returns true 
// if n is perfect
static bool isPerfect(int n)
{
      
    // Variable to store sum of
    // divisors
    int sum = 1;
  
    // Find all divisors and add them
    for(int i = 2; i * i <= n; i++) 
    {
       if (n % i == 0) 
       {
           if (i * i != n)
               sum = sum + i + n / i;
           else
               sum = sum + i;
       }
    }
  
    // Check if sum of divisors is equal 
    // to n, then n is a perfect number
    if (sum == n && n != 1)
        return true;
    return false;
}
  
// Function to perform dfs
static void dfs(int node, int parent)
{
  
    // If weight of the current node
    // is a perfect number
    if (isPerfect(weight[node]))
        ans += 1;
  
    foreach(int to in graph[node]) 
    {
        if (to == parent)
            continue;
        dfs(to, node);
    }
}
  
// Driver code
public static void Main(String[] args)
{
  
    for(int i = 0; i < graph.Length; i++)
       graph[i] = new List<int>();
          
    // Weights of the node
    weight[1] = 5;
    weight[2] = 10;
    weight[3] = 11;
    weight[4] = 8;
    weight[5] = 6;
  
    // Edges of the tree
    graph[1].Add(2);
    graph[2].Add(3);
    graph[2].Add(4);
    graph[1].Add(5);
  
    dfs(1, 1);
    Console.Write(ans);
}
}
  
// This code is contributed by amal kumar choubey

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Output:

1

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