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:
Output: 3
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 <bits/stdc++.h> using namespace std;
int ans = 0;
vector< int > graph[100];
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[1] = 4;
weight[2] = 5;
weight[3] = 3;
weight[4] = 25;
weight[5] = 16;
weight[6] = 30;
// Edges of the tree
graph[1].push_back(2);
graph[2].push_back(3);
graph[2].push_back(4);
graph[1].push_back(5);
graph[5].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<Integer>[] 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[100];
static int [] weight = new int [100];
// 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[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);
Console.Write(ans);
} } // This code is contributed by rutvik_56 |
Javascript
<script> // Javascript implementation of the approach let ans=0;
let graph = new Array(100);
let weight = new Array(100);
for (let i=0;i<100;i++)
{
graph[i]=[];
weight[i]=0;
}
// Function that returns true
// if n is a perfect square
function isPerfectSquare(n)
{
let x = Math.sqrt(n);
if (Math.floor(x) != Math.ceil(x))
return false ;
return true ;
}
// Function to perform dfs
function dfs(node,parent)
{
// If weight of the current node
// is a perfect square
if (isPerfectSquare(weight[node]))
ans += 1;
for (let to=0;to<graph[node].length;to++)
{
if (graph[node][to] == parent)
continue
dfs(graph[node][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].push(2);
graph[2].push(3);
graph[2].push(4);
graph[1].push(5);
graph[5].push(6);
dfs(1, 1);
document.write( ans);
// This code is contributed by unknown2108
</script> |
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.