The Skyline Problem
code-golf, rosetta-stone
Solution
I'm just starting to learn J, so here goes my first attempt at golf:
103 62 49 46 characters
b =: 8 3 $ 1 11 5 2 6 7 3 13 9 12 7 16 14 3 25 19 18 22 23 13 29 24 4 28
,(,.{&s)I.s~:_1|.s=:0,~>./(1&{*{.<:[:i.{:)"1 b
1 11 3 13 9 0 12 7 16 3 19 18 22 3 23 13 29 0
although I'm sure someone who actually knows the language well could shorten this by quite a bit
An explanation of the code:
NB. list numbers up to right bound of the building
([: i. {:) 14 3 25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
NB. compare to left bound of building and then multiply by height
(1&{ * {. <: [: i. {:) 14 3 25
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3
NB. apply to each row of b, note how shorter entries are padded with 0s
(1&{ * {. <: [: i. {:)"1 b
0 11 11 11 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 6 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
...
NB. collapse to find max, add a 0 to the end for rotate later, assign to s
] s =: 0 ,~ >./ (1&{ * {. <: [: i. {:)"1 b
0 11 11 13 13 13 13 13 13 0 0 0 7 7 7 7 3 3 3 18 18 18 3 13 13 13 13 13 13 0
NB. rotate s right 1 and then compare to s to find where height changes
s ~: _1 |. s
0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1
NB. find indices of all differences
I. s ~: _1 |. s
1 3 9 12 16 19 22 23 29
NB. pair each index with the height of the building there
(,. {&s) I. s ~: _1 |. s
1 11
3 13
9 0
...
NB. and finally flatten the list
, (,. {&s) I. s ~: _1 |. s
1 11 3 13 9 0 12 7 16 3 19 18 22 3 23 13 29 0
Problem
I just came across this little problem on UVA's Online Judge and thought, that it may be a good candidate for a little code-golf. The problem: You are to design a program to assist an architect in drawing the skyline of a city given the locations of the buildings in the city. To make the problem tractable, all buildings are rectangular in shape and they share a common bottom (the city they are built in is very flat). The city is also viewed as two-dimensional. A building is specified by an ordered triple (Li, Hi, Ri) where Li and Ri are left and right coordinates, respectively, of building i and Hi is the height of the building. In the diagram below buildings are shown on the left with triples ``` (1,11,5), (2,6,7), (3,13,9), (12,7,16), (14,3,25), (19,18,22), (23,13,29), (24,4,28) ``` and the skyline, shown on the right, is represented by the sequence: ``` 1, 11, 3, 13, 9, 0, 12, 7, 16, 3, 19, 18, 22, 3, 23, 13, 29, 0 ``` The output should consist of the vector that describes the skyline as shown in the example above. In the skyline vector (v1, v2, v3, ... vn) , the vi such that i is an even number represent a horizontal line (height). The vi such that i is an odd number represent a vertical line (x-coordinate). The skyline vector should represent the "path" taken, for example, by a bug starting at the minimum x-coordinate and traveling horizontally and vertically over all the lines that define the skyline. Thus the last entry in the skyline vector will be a 0. The coordinates must be separated by a blank space. If I will not count declaration of provided (test) buildings and including all spaces and tab characters, my solution, in Python, is 223 characters long. Here is the condensed version: ``` B=[[1,11,5],[2,6,7],[3,13,9],[12,7,16],[14,3,25],[19,18,22],[23,13,29],[24,4,28]] # Solution. R=range v=[0 for e in R(max([y[2] for y in B])+1)] for b in B: for x in R(b[0], b[2]): if b[1]>v[x]: v[x]=b[1] p=1 k=0 for x in R(len(v)): V=v[x] if p and V==0: continue elif V!=k: p=0 print "%s %s" % (str(x), str(V)), k=V ``` I think that I didn't made any mistake but if so - feel free to criticize me. I don't have much reputation, so I will pay only 100 for a bounty - I am curious, if anyone could try to solve this in less than .. lets say, 80 characters. Solution posted by cobbal is 101 characters long and currently it is the best one. I thought, that 80 characters is a sick limit for this kind of problem. cobbal, with his 46 character solution totaly amazed me - though I must admit, that I spent some time reading his explanation before I partially understood what he had written.