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++
// 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 arrayvoid 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 codeint main(){ int N = 6; constructArray(N); return 0;} |
Java
// Java program to construct array// that cube sum of all element// is a perfect squareimport java.util.*;class GFG{// Function to create// and print the arraystatic 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 codepublic static void main(String[] args){ int N = 6; constructArray(N);}}// This code is contributed by AbhiThakur |
Python3
# 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#
// C# program to construct array// that cube sum of all element// is a perfect squareusing System;class GFG{// Function to create// and print the arraystatic 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 codepublic static void Main(){ int N = 6; constructArray(N);}}// This code is contributed by Code_Mech |
Javascript
<script>// JavaScript program to construct an array// that cube sum of all element// is a perfect square// Function to create// and print the arrayfunction 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 codelet N = 6;constructArray(N);// This code is contributed by Manoj.</script> |
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.
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