CCC 2003 Stage1: J2: Picture Perfect

[Tony]

Roy has a stack of student yearbook photos. He wants to lay the pictures on a flat sufrace edge-to-edge to form a filled rectangle with minimum perimeter. All photos must by fully visible. Each picture is a square with dimentions 1 unit by 1 unit.
For example, he would place 12 photos in the following configuration, where each photo is indicated with an X

XXXX
XXXX
XXXX

ofcourse, he could orient them in the other direction, such as

XXX
XXX
XXX
XXX

which would have teh same perimeter, 14 units.

Your problem should be interactive. It should repeatedly read a positive integer C, the number of pictures to be laid out. For each input, it should print the smallest possible perimeter for a filled rectangle that is formed by laying alla the pictures edge-to-edge. Also print the dimensions of this rectangle.

You may assuem that there are less than 65,000 photos. An input value of C=0 indicated that the program should terminate.

Sample Session
Enter number of pictures:
100
Minumum perimeter is 40 with dimensions 10x10

Enter number of pictures:
15
Minumum perimeter is 16 with dimensions of 3x5

Enter number of pictures:
195
Minumun perimeter is 56 with dimensions 13x15

Enter number of pictures:
0

Solution by JSBN

code:

%LARGER AMOUNTS OF PICTURES WILL REQUIRE MORE TIME FOR CALCULATION var C : int var z : int var t2 : int var d1 : int var d2 : int loop     put "Enter number of pictures"     get C     t2 := 65000     exit when C = 0     for i1 : 1 .. C         for i2 : 1 .. C             z := i1 * i2             if z = C then                 if (i1 + i2) * 2 <= t2 then                     t2 := (i1 + i2) * 2                     d1 := i1                     d2 := i2                     exit                 end if             end if         end for     end for     put "Minimum Perimeter is ", t2, " with the dimensions ", d1, " X ", d2     put "" end loop

I wish he would comment his solutions basically two loops run through every possible rectangle size and just keeps track of the smallest perimeter it finds. Simple and easy.

[Dan]

i whode like to know how you whode do this if 64,999 is entred as a number. becuse that was one of the test values for the test. i lost a few points becuse my progame did not finsh in time.

[Tony]

rofl, If you would run my substring (S4) for those half a million char values... it would take a day for a single set... fortunatly (well for the teacher, not me) the program didnt execute over 65K solutions so it worked for 3/5 cases taking just few minutes each.

Edit: Doesnt answer your question, but something nice to know... the thing was inpossible in turing anyway as input for 4/5 cases was over 256 chars in length

[octopi]

Dan the number was acctually different, it wasn't 64999, it was a prime number 63907 I think it was. Anyways, as we know prime numbers only have 1, and themselves as factors. So it was kind of cheap of them to do that, I can't see many people passing that, unless there teachers let it run for days.

Any one else have any ideas on how to speed that one up?

[Office of the Registar]

i think i have that was pretty short
let me look for it...