| The Skyline Problem |
With the advent of high speed graphics workstations, CAD (computer-aided design) and other areas (CAM, VLSI design) have made increasingly effective use of computers. One of the problems with drawing images is the elimination of hidden lines -- lines obscured by other parts of a drawing.
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 
where
and 
are left and right coordinates, respectively, of building
i and 
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)
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 input is a sequence of building triples. All coordinates of
buildings are integers less than 10,000 and there will be at least one
and at most 50 buildings in the input file. Each building triple is on
a line by itself in the input file. All integers in a triple are
separated by one or more spaces. The triples will be sorted by ,
the left x-coordinate of the building, so the building
with the smallest left x-coordinate is
first in the input file.
The output should consist of the vector that describes the skyline as
shown in the example above. In the skyline vector 
, the 
such that i is an even number
represent a horizontal line (height). The 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 all
skyline vectors will be a 0.
1 11 5 2 6 7 3 13 9 12 7 16 14 3 25 19 18 22 23 13 29 24 4 28
1 11 3 13 9 0 12 7 16 3 19 18 22 3 23 13 29 0