A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker (i. e. every even numbered locker). Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. StudentS5 starts with L5 and changes every fifth locker, and so on, until student S100 changes L100.After all the students have passed through the building and changed the lockers, which lockers areopen? Write a program to find your answer.(Hint: Use an array of 100 boolean elements. each of which indicates whether a locker is open (true) or closed (false). Initially, all lockers are closed.)

Solution :

public class NewMain {  

   public_static void main_(String[] args) {  

       boolean[] _locker = new boolean_[101];  

       // to set all the locks to a false NOTE:  first locker is the number 0. Last locker is the 99.

       for (int_i=1;i<locker_length; i++)

       {

       locker[i] = false;

       }

       // first student opens all lockers.

       for (int i=1;i<locker.length; i++)        {

       locker[i] = true;

       }

       for(int S=2; S<locker.length; S++)

       {

          for(int k=S; k<locker.length; k=k+S)

          {

              if(locker[k]==false) locker[k] = true;

              else locker[k] = false;      

          }            

       }

       for(int S=1; S<locker.length; S++)

       {

           if (locker[S] == true) {

               System.out.println("Locker " + S + " Open");

           }

         /* else {

               System.out.println("Locker " + S + " Close");

           } */

       }

   }

}

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