构造一个大小为 N 的数组，其所有元素的立方和是一个完全平方数

给定一个整数N ，任务是构造一个大小为N的排序数组arr[] ，使得所有元素的立方和是一个完美的平方，即$\sum_{}A_i^3=X^2$ ，其中 X 是整数。

例子：

Input: N = 5 
Output: 1 2 3 4 5 
Explanation 
Sum of cube of all elements = 1 + 8 + 27 + 64 + 125 = 225 
which is a perfect square number.

Input: N = 1 
Output: 1 
 

解决方法：

1. 前 N 个自然数的立方和由下式给出：
   $(\frac{N \times(N+1)}{2})^2$
2. 所以，总和本身就是整数的完美平方$X^2&=(\frac{N \times(N+1)}{2})^2$
3. 所以$X&=(\frac{N \times(N+1)}{2})$ ，它只不过是 N 个自然数的和。
4. 因此，只需打印前 N 个自然数来构造数组。

下面是上述方法的实现：

C++

// C++ implementation of the
// above approach
 
#include 
using namespace std;
 
// Function to construct an array
// of size N
void constructArray(int N)
{
    for (int i = 1; i <= N; i++) {
 
        // Prints the first N
        // natural numbers
        cout << i << " ";
    }
}
 
// Driver code
int main()
{
    int N = 5;
    constructArray(N);
    return 0;
}

Java

// Java implementation of the
// above approach
class GFG{
     
// Function to construct an array
// of size N
public static void constructArray(int N)
{
    for(int i = 1; i <= N; i++)
    {
        
       // Prints the first N
       // natural numbers
       System.out.print(i + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 5;
    constructArray(N);
}
}
 
// This code is contributed by divyeshrabadiya07

Python3

# Python3 implementation of the
# above approach
 
# Function to construct an array
# of size N
def constructArray(N):
     
    for i in range(1, N + 1):
         
        # Prints the first N
        # natural numbers
        print(i, end = ' ')
         
 
# Driver code
if __name__=='__main__':
     
    N = 5
     
    constructArray(N)
 
# This code is contributed by rutvik_56

C#

// C# implementation of the
// above approach
using System;
class GFG{
     
// Function to construct an array
// of size N
public static void constructArray(int N)
{
    for(int i = 1; i <= N; i++)
    {
         
        // Prints the first N
        // natural numbers
        Console.Write(i + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    int N = 5;
    constructArray(N);
}
}
 
// This code is contributed by sapnasingh4991

Javascript

 
// JavaScript implementation of the
// above approach
 
// Function to construct an array
// of size N
function constructArray(N)
{
    for(let i = 1; i <= N; i++)
    {
         
        // Prints the first N
        // natural numbers
        document.write(i + " ");
    }
}
 
// Driver code
let N = 5;
 
constructArray(N);
 
// This code is contributed by Surbhi Tyagi.
 

输出：

1 2 3 4 5

时间复杂度： O(N)
辅助空间： O(1)