100 doors

From Fōrmulæ wiki
Jump to: navigation, search

This page is the answer to the task 100 doors in the Rosetta Code.

Description (from Rosetta Code)

There are 100 doors in a row that are all initially closed.

You make 100 passes by the doors.

The first time through, visit every door and  toggle  the door  (if the door is closed,  open it;   if it is open,  close it).

The second time, only visit every 2nd door   (door #2, #4, #6, ...),   and toggle it.

The third time, visit every 3rd door   (door #3, #6, #9, ...), etc,   until you only visit the 100th door.

Task

Answer the question: what state are the doors in after the last pass? Which are open, which are closed?

Alternate: As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.

Opening only those doors is an optimization that may also be expressed; however, as should be obvious, this defeats the intent of comparing implementations across programming languages.

Program

100Doors.png

Results

100DoorsOutput1.png

Showing the intermediate states

Ir requires a small change to the original program.

100Doors2.png

(image has been reduced in size)

100Doors2Output.png