Can someone help me solve this problem in C#?

Question

There is a number 1 written on the board. We have a sequence a of n natural numbers, and in the i-th step (1 ≤ i ≤ n), we erase the current number on the board and replace it with the product of that number and the number a[i]. After each step, determine whether the current number on the board is a perfect square.

Input

The first line of standard input contains a natural number n (1 ≤ n ≤ 10,000) representing the length of the sequence a. The next line contains n natural numbers (between 1 and 1 billion) separated by spaces, which are the elements of the sequence a in the order they are multiplied by the current number on the board.

Output

For each element of the sequence a, in the order of input, print yes if its product with the current number on the board is a perfect square, otherwise print no. Time limit is 0,1 seconde

Answer 1

To solve this problem, you need to keep track of the number on the board as it is updated by multiplying it with each element from the sequence a, and after each step, we must check if the resulting number is a perfect square.

Pseudocode:

1. Read the input.
2. Start with the number 1 on the board.
3. For each element in the sequence, multiply it with the current number on the board and check if the result is a perfect square.
4. Output "yes" or "no" based on whether the current product is a perfect square.

using System;
class PerfectSquareChecker
{
    // Helper function to check if a number is a perfect square
    static bool IsPerfectSquare(long x)
    {
        if (x < 0) return false;
        long sqrtX = (long)Math.Sqrt(x);
        return sqrtX * sqrtX == x;
    }
    static void Main()
    {
        // Read the input
        int n = int.Parse(Console.ReadLine());  // Number of elements in the sequence
        string[] input = Console.ReadLine().Split();  // Sequence of numbers as strings
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
        {
            a[i] = long.Parse(input[i]);  // Parse each element into a long array
        }
        // Start with 1 on the board
        long currentNumber = 1;
        // Process each number in the sequence
        for (int i = 0; i < n; i++)
        {
            currentNumber *= a[i];  // Multiply current number with a[i]
            
            // Check if the current number is a perfect square
            if (IsPerfectSquare(currentNumber))
            {
                Console.WriteLine("yes");
            }
            else
            {
                Console.WriteLine("no");
            }
        }
    }
}

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hth

Marcin