Given the size of array N, the task is to construct an array of size N with positive integer elements such that the cube sum of all elements of this array is a perfect square.
Note: Repetitions of integers are allowed.
Example:
Input: N = 1
Output: 4
Explanation: Cube of 4 is 64, and 64 is perfect square.
Input: N = 6
Output: 5 10 5 10 5 5
Explanation: Cubic sum of array element is (5)3 + (10)3 + (5)3 + (10)3 + (5)3 + (5)3 = 2500, and 2500 is perfect square.
Approach: The idea is to construct array of size, N which contain first N natural number. If closely observed,
cubic sum of first N natural number: (1)3 + (2)3 + (3)3 + (4)3 + …….(N)3 is always perfect square.
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Below is the implementation of the above approach.
// C++ program to construct an array // that cube sum of all element // is a perfect square #include <bits/stdc++.h> using namespace std;
// Function to create // and print the array void constructArray( int N)
{ int arr[N];
// initialise the array of size N
for ( int i = 1; i <= N; i++) {
arr[i - 1] = i;
}
// Print the array
for ( int i = 0; i < N; i++) {
cout << arr[i] << ", " ;
}
} // Driver code int main()
{ int N = 6;
constructArray(N);
return 0;
} |
// Java program to construct array // that cube sum of all element // is a perfect square import java.util.*;
class GFG{
// Function to create // and print the array static void constructArray( int N)
{ int arr[] = new int [N];
// Initialise the array of size N
for ( int i = 1 ; i <= N; i++)
{
arr[i - 1 ] = i;
}
// Print the array
for ( int i = 0 ; i < N; i++)
{
System.out.print(arr[i] + ", " );
}
} // Driver code public static void main(String[] args)
{ int N = 6 ;
constructArray(N);
} } // This code is contributed by AbhiThakur |
# Python3 program to construct # array that cube sum of all # element is a perfect square # Function to create # and print the array def constructArray(N):
arr = [ 0 ] * N
# Initialise the array of size N
for i in range ( 1 , N + 1 ):
arr[i - 1 ] = i;
# Print the array
for i in range (N):
print (arr[i], end = ", " )
# Driver code N = 6 ;
constructArray(N); # This code is contributed by grand_master |
// C# program to construct array // that cube sum of all element // is a perfect square using System;
class GFG{
// Function to create // and print the array static void constructArray( int N)
{ int []arr = new int [N];
// Initialise the array of size N
for ( int i = 1; i <= N; i++)
{
arr[i - 1] = i;
}
// Print the array
for ( int i = 0; i < N; i++)
{
Console.Write(arr[i] + ", " );
}
} // Driver code public static void Main()
{ int N = 6;
constructArray(N);
} } // This code is contributed by Code_Mech |
<script> // JavaScript program to construct an array // that cube sum of all element // is a perfect square // Function to create // and print the array function constructArray(N)
{ let arr = new Array(N);
// initialise the array of size N
for (let i = 1; i <= N; i++)
{
arr[i - 1] = i;
}
// Print the array
for (let i = 0; i < N; i++)
{
document.write(arr[i] + ", " );
}
} // Driver code let N = 6; constructArray(N); // This code is contributed by Manoj. </script> |
Output:
1, 2, 3, 4, 5, 6,
Time Complexity: O(N) where N is the size of the Array.
Space Complexity: O(N), for creating an array to store the answer.