Question

The Lockers Problem There is a well-known mathematical logic problem called the lockers problem. Here is a description of the problem 23 24 25 26 A new high school has just opened! There are 50 lockers in the school and they have been numbered from 1 through 50. When the school opens the first student to enter the school walks into the hallway and opens all the locker doors! Afterwards, the second student closes each door whose number is a multiple of 2. Similarly, the third student changes every door that is a multiple of 3 (closing open doors, opening closed doors). The fourth student changes each door that is a multiple of 4 and so on. After 50 students have entered the hallway, which locker doors are open? Using your BitArray class described above, solve the lockers problem. Each bit in your BitArray should represent a locker, where true is an open locker and false is a closed locker. Once you have finished altering each bit according to the problem statement, print out the number and state of each locker, for example: 1: open 2: CLosed 3: closed 4: open 5. closed 6. closed 7. closed

Answer 1

The question did not specify language so i have implement it in C++ using array

code :

# include <bits/stdc++.h>
using namespace std;
int arr[51];
int main()
{
   int i,j;
   for(i=1;i<=50;i++)
       for(j=i;j<=50;j+=i)
           arr[j] = 1 - arr[j];       //Flip state of all lockers multiple of i

   for(i=1;i<=50;i++)
       cout << i <<": " << (arr[i]? "open" : "closed") << "\n";
}