Write a program, solving problem below in any new for you language:
There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; next the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers closed, closes lockers open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and so on. This goes on until every student has had a turn. How many lockers will be open at the end? What is the formula?
Find solution in Dart below:
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| import 'dart:io'; | |
| int numberOfLockers = 1000; | |
| // Lockers start all open because of the first student | |
| List<String> lockers = new List.filled(numberOfLockers + 1, 'open'); | |
| main() { | |
| for (var student = 2; student <= numberOfLockers; student++) { | |
| // For the student, open the locker if closed, or close if open | |
| for (var locker = student; locker <= numberOfLockers; locker += student) { | |
| lockers[locker] = lockers[locker] == 'open' ? 'closed' : 'open'; | |
| } | |
| } | |
| // Count of lockers remaining open | |
| int total = 0; | |
| // List the lockers that remain open | |
| for (var locker = 1; locker <= numberOfLockers; locker ++ ) { | |
| if (lockers[locker] == 'open') { | |
| stdout.write("${locker} "); | |
| total += 1; | |
| } | |
| } | |
| print("\nThere are ${total} lockers remaining open."); | |
| } | |
| // 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 961 | |
| // There are 31 lockers remaining open. |