TopCoder problem "Solid" used in TCCC '04 Round 2 (Division I Level One)



Problem Statement

    

The solid in the picture below is made up of 1x1x1 cubes in a 3D grid. In this problem, we'll limit ourselves to solids that are made up of columns rooted on the ground (a column consists of one or several 1x1x1 cubes stacked on top of each other). Such solids can be described as a String[] of digits, where each digit corresponds to the height of a column in the 2D grid that makes up the ground. A zero means there is no column at all in that position.

The solid in the picture would thus be described like this: (quotes for clarity only) 

{"4231",
 "2101",
 "0001"}


The volume of such a solid is simple enough to calculate, but we're interested here in the surface area (that is, the number of 1x1 "squares" on the outer surface). Create a class Solid containing the method surfaceArea which takes a String[] solid in the format mentioned aboved and returns an int, the surface area of this solid. You can assume that the solid is connected, i.e the columns will be attached to each other in the four cardinal directions.

 

Definition

    
Class:Solid
Method:surfaceArea
Parameters:String[]
Returns:int
Method signature:int surfaceArea(String[] solid)
(be sure your method is public)
    
 

Constraints

-solid will contain between 1 and 50 elements, inclusive.
-Each element in solid will contain between 1 and 50 characters, inclusive.
-All elements in solid will have the same number of characters.
-All characters in solid will be digits, '0'-'9'.
-solid will describe one single, connected solid.
-The volume of the solid will be at least 1.
 

Examples

0)
    
{"11"}
Returns: 10
This is just a 2x1x1 solid. It has six sides, four of them with surface area 2 and two with suface area 1. The total surface area is therefore 10.
1)
    
{"4231",
 "2101",
 "0001"}
Returns: 54
This is the solid in the picture in the problem statement.
2)
    
{"0000000000000000000",
 "0000000111111111100",
 "0001111111111111100",
 "0111111222111110000",
 "0111111122111111000",
 "0111111111111111000",
 "0000000000000000000"}
Returns: 190
3)
    
{"000000528711731016006000000000",
 "000005195794786382818000000000",
 "000000152759877615783700000000",
 "000000538691532646444720000000",
 "000448878233764358916526040000",
 "000957681868472329823514746000",
 "000468262265258953611195968000",
 "353414949614353741985971227000",
 "523414326739461146956185360000", 
 "883755114476244883219144444000",
 "382853216452287831155934152000",
 "582346653747546124514813113000",
 "872646187355968637442125842000",
 "488795678641528974985428554900",
 "184834779675978184943349141300",
 "466455559389179259181268463686",
 "577566824847934671312749443414",
 "879443115123574825441232482522",
 "813346335659785489878484611130",
 "913125858434291686688282682100",
 "276982916388781784196666212965",
 "171998843675177318752563287763",
 "639855577925843147586517873468",
 "527868897287142566166897778388",
 "513544481355194141741396768845",
 "148819842161491541656585512420",
 "014784988399688355411932978550",
 "008427963354683469419487790000",
 "007889062567387593411210000000",
 "000000005778849898967400000000"}
Returns: 6280
4)
    
{"111",
 "101",
 "111"}
Returns: 32
5)
    
{"5"}
Returns: 22

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2290

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5007&pm=2290

Writer:

Yarin

Testers:

lbackstrom , schveiguy

Problem categories:

Geometry