The Curious Case Of Benjamin Bulbs

Faq

Q1) Why only perfect square are on after the nth number of fluctuation ?
ans: All perfect square numbers have odd numbers of factors so it will be on after nth number of fluctuation.

Q2) Why is the condition i*i<=n ?
ans: Since we are checking only the perfect square that why we are checking the condition for square.

Q3) what will the time complexity and space complexity ?
ans: time complexity : O(logn)
     Space complexity : O(1)

Hints

Hint 1: Do a dry run for 20 bulbs with 20 fluctuation and try to see the pattern .

Hint 2: Check for number with odd numbers of factor.

Hint 3: All perfect square number have odd number of factors.

Hint 4: All perfect square number will be on.

Mcq

Q1) fill the blank for this problem ?

    for(int i = 1; ______ ; i++)
        {
            System.out.println(i * i);
        }
    
    a) i<=n
    b) i<n
    c) i*i<n
    d) i*i<=n

ans: d) i*i<=n

Q2) What is the time complexity for this code?

    1. O(N)
    2. O(N^2)
    3. O(1)
    4. O(log N)
    
ans: 4)

Q3) What will be the output for 23?
    
    a) 1 4 9 16
    b) 1 2 6 7
    c) 1 4 9 16 24
    d) 1 3 5 6 9
    
ans: a)