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++

`// 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; ` `} ` |

## Java

`// 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 ` |

## C#

`// 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 ` |

## Python3

`# 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 ` |

**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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