Count the nodes in the given tree whose weight is a power of two

Given a tree, and the weights of all the nodes, the task is to count the number of nodes whose weight is a power of 2.

Examples:

Input:

Output: 1
Only the weight of the node 4 is a power of 2.

Approach: Perform dfs on the tree and for every node, check if its weight is a power of 2 or not, if yes then increment the count.

Below is the implementation of the above approach:

C++



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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
int ans = 0;
  
vector<int> graph[100];
vector<int> weight(100);
  
// Function to perform dfs
void dfs(int node, int parent)
{
    // If weight of the current node
    // is a power of 2
    int x = weight[node];
    if (x && (!(x & (x - 1))))
        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 of the approach 
import java.util.*;
  
class GFG 
{
  
    static int ans = 0;
  
    @SuppressWarnings("unchecked")
    static Vector<Integer>[] graph = new Vector[100];
    static int[] weight = new int[100];
  
    // Function to perform dfs
    static void dfs(int node, int parent)
    {
        // If weight of the current node
        // is a power of 2
        int x = weight[node];
        if (x != 0 && (x & (x - 1)) == 0)
            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 < 100; i++)
            graph[i] = new Vector<>();
  
        // 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.println(ans);
    }
}
  
// This code is contributed by
// sanjeev2552

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C#

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// C# implementation of the approach 
using System; 
using System.Collections.Generic; 
  
class GFG 
      
static int ans = 0; 
static List<List<int>> graph = new List<List<int>>(); 
static List<int> weight = new List<int>(); 
  
// Function to perform dfs 
static void dfs(int node, int parent) 
  
    // If weight of the current node 
    // is a power of 2 
    int x = weight[node]; 
    bool result = Convert.ToBoolean((x & (x - 1)));
    bool result1 = Convert.ToBoolean(x);
    if (result1 && (!result)) 
        ans += 1; 
  
    for (int i = 0; i < graph[node].Count; i++) 
    
        if (graph[node][i] == parent) 
            continue
        dfs(graph[node][i], node); 
    
  
// Driver code 
public static void Main(String []args) 
    // Weights of the node 
    weight.Add(0); 
    weight.Add(5); 
    weight.Add(10);; 
    weight.Add(11);; 
    weight.Add(8); 
    weight.Add(6); 
      
    for(int i = 0; i < 100; i++) 
    graph.Add(new List<int>()); 
  
    // Edges of the tree 
    graph[1].Add(2); 
    graph[2].Add(3); 
    graph[2].Add(4); 
    graph[1].Add(5); 
  
    dfs(1, 1); 
  
    Console.WriteLine(ans); 
  
// This code is contributed by shubhamsingh10

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Python3

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# Python3 implementation of the approach
ans = 0
  
graph = [[] for i in range(100)] 
weight = [0]*100
  
# Function to perform dfs 
def dfs(node, parent):
    global mini, graph, weight, ans 
      
    # If weight of the current node 
    # is a power of 2 
    x = weight[node]
    if (x and (not (x & (x - 1)))):
        ans += 1
    for to in graph[node]: 
        if (to == parent): 
            continue
        dfs(to, node) 
          
        # Calculating the weighted 
        # sum of the subtree 
        weight[node] += weight[to] 
      
# Driver code
  
# 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].append(2)
graph[2].append(3)
graph[2].append(4)
graph[1].append(5)
  
dfs(1, 1)
print(ans)
  
# This code is contributed by SHUBHAMSINGH10

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Output:

1

Complexity Analysis:

  • Time Complexity: O(N).
    In DFS, every node of the tree is processed once and hence the complexity due to the DFS is O(N) for N nodes in the tree. Therefore, the time complexity is O(N).
  • Auxiliary Space: O(1).
    Any extra space is not required, so the space complexity is constant.

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