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# Count the nodes whose weight is a perfect square

• Last Updated : 20 Apr, 2021

Given a tree, and the weights of all the nodes, the task is to count the number of nodes whose weight is a perfect Square.
Examples:

Input:

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Only the weights of nodes 1, 4 and 5 are perfect squares.

Approach: Perform dfs on the tree and for every node, check if it’s weight is a perfect square or not.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `int` `ans = 0;` `vector<``int``> graph;``vector<``int``> weight(100);` `// Function that returns true``// if n is a perfect square``bool` `isPerfectSquare(``int` `n)``{``    ``double` `x = ``sqrt``(n);``    ``if` `(``floor``(x) != ``ceil``(x))``        ``return` `false``;``    ``return` `true``;``}` `// Function to perform dfs``void` `dfs(``int` `node, ``int` `parent)``{``    ``// If weight of the current node``    ``// is a perfect square``    ``if` `(isPerfectSquare(weight[node]))``        ``ans += 1;` `    ``for` `(``int` `to : graph[node]) {``        ``if` `(to == parent)``            ``continue``;``        ``dfs(to, node);``    ``}``}` `// Driver code``int` `main()``{``    ``int` `x = 15;` `    ``// Weights of the node``    ``weight = 4;``    ``weight = 5;``    ``weight = 3;``    ``weight = 25;``    ``weight = 16;``    ``weight = 30;` `    ``// Edges of the tree``    ``graph.push_back(2);``    ``graph.push_back(3);``    ``graph.push_back(4);``    ``graph.push_back(5);``    ``graph.push_back(6);` `    ``dfs(1, 1);` `    ``cout << ans;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG{`` ` `static` `int` `ans = ``0``;`` ` `static` `Vector[] graph = ``new` `Vector[``100``];``static` `int``[] weight = ``new` `int``[``100``];`` ` `// Function that returns true``// if n is a perfect square``static` `boolean` `isPerfectSquare(``int` `n)``{``    ``double` `x = Math.sqrt(n);``    ``if` `(Math.floor(x) != Math.ceil(x))``        ``return` `false``;``    ``return` `true``;``}`` ` `// Function to perform dfs``static` `void` `dfs(``int` `node, ``int` `parent)``{``    ``// If weight of the current node``    ``// is a perfect square``    ``if` `(isPerfectSquare(weight[node]))``        ``ans += ``1``;`` ` `    ``for` `(``int` `to : graph[node]) {``        ``if` `(to == parent)``            ``continue``;``        ``dfs(to, node);``    ``}``}`` ` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `x = ``15``;``    ``for` `(``int` `i = ``0``; i < ``100``; i++)``        ``graph[i] = ``new` `Vector<>();``    ` `    ``// Weights of the node``    ``weight[``1``] = ``4``;``    ``weight[``2``] = ``5``;``    ``weight[``3``] = ``3``;``    ``weight[``4``] = ``25``;``    ``weight[``5``] = ``16``;``    ``weight[``6``] = ``30``;`` ` `    ``// Edges of the tree``    ``graph[``1``].add(``2``);``    ``graph[``2``].add(``3``);``    ``graph[``2``].add(``4``);``    ``graph[``1``].add(``5``);``    ``graph[``5``].add(``6``);`` ` `    ``dfs(``1``, ``1``);`` ` `    ``System.out.print(ans);``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach``from` `math ``import` `*``ans ``=` `0` `graph ``=` `[[] ``for` `i ``in` `range``(``100``)]``weight ``=` `[``0``] ``*` `100` `# Function that returns true``# if n is a perfect square``def` `isPerfectSquare(n):``    ``x ``=` `sqrt(n)``    ``if` `(floor(x) !``=` `ceil(x)):``        ``return` `False``    ``return` `True` `# Function to perform dfs``def` `dfs(node, parent):``    ``global` `ans``    ` `    ``# If weight of the current node``    ``# is a perfect square``    ``if` `(isPerfectSquare(weight[node])):``        ``ans ``+``=` `1``;``    ` `    ``for` `to ``in` `graph[node]:``        ``if` `(to ``=``=` `parent):``            ``continue``        ``dfs(to, node)` `# Driver code` `x ``=` `15` `# Weights of the node``weight[``1``] ``=` `4``weight[``2``] ``=` `5``weight[``3``] ``=` `3``weight[``4``] ``=` `25``weight[``5``] ``=` `16``weight[``6``] ``=` `30` `# Edges of the tree``graph[``1``].append(``2``)``graph[``2``].append(``3``)``graph[``2``].append(``4``)``graph[``1``].append(``5``)``graph[``5``].append(``6``)` `dfs(``1``, ``1``)``print``(ans)` `# This code is contributed by SHUBHAMSINGH10`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections;``using` `System.Collections.Generic;``using` `System.Text;` `class` `GFG{``    ` `static` `int` `ans = 0;` `static` `ArrayList[] graph = ``new` `ArrayList;``static` `int``[] weight = ``new` `int``;` `// Function that returns true``// if n is a perfect square``static` `bool` `isPerfectSquare(``int` `n)``{``    ``double` `x = Math.Sqrt(n);``    ` `    ``if` `(Math.Floor(x) != Math.Ceiling(x))``        ``return` `false``;``        ` `    ``return` `true``;``}` `// Function to perform dfs``static` `void` `dfs(``int` `node, ``int` `parent)``{``    ` `    ``// If weight of the current node``    ``// is a perfect square``    ``if` `(isPerfectSquare(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)``{``    ``//int x = 15;``    ``for``(``int` `i = 0; i < 100; i++)``        ``graph[i] = ``new` `ArrayList();``    ` `    ``// Weights of the node``    ``weight = 4;``    ``weight = 5;``    ``weight = 3;``    ``weight = 25;``    ``weight = 16;``    ``weight = 30;` `    ``// Edges of the tree``    ``graph.Add(2);``    ``graph.Add(3);``    ``graph.Add(4);``    ``graph.Add(5);``    ``graph.Add(6);` `    ``dfs(1, 1);` `    ``Console.Write(ans);``}``}` `// This code is contributed by rutvik_56`

## Javascript

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Output:
`3`

Complexity Analysis:

• Time Complexity: O(N*logV) where V is the maximum weight of a node in the tree.
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. Also, while processing every node, in order to check if the node value is a perfect square or not, the inbuilt sqrt(V), is being called where V is the weight of the node and this function has a complexity of O(log V). Hence for every node, there is an added complexity of O(log V). Therefore, the total time complexity is O(N*logV).
• Auxiliary Space: O(1).
Any extra space is not required, so the space complexity is constant.

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