The construction of office buildings has become a very standardized task. Pre-fabricated
modules are combined according to the customer’s needs, shipped from a faraway factory,
and assembled on the construction site. However, there are still some tasks that require
careful planning, one example being the routing of pipes for the heating system.
A modern office building is made up of square modules, one on each floor being a service
module from which (among other things) hot water is pumped out to the other modules
through the heating pipes. Each module (including the service module) will have heating
pipes connecting it to exactly two of its two to four neighboring modules. Thus, the pipes
have to run in a circuit, from the service module, visiting each module exactly once, before
finally returning to the service module. Due to different properties of the modules, having
pipes connecting a pair of adjacent modules comes at different costs. For example, some
modules are separated by thick walls, increasing the cost of laying pipes. Your task is to,
given a description of a floor of an office building, decide the cheapest way to route the
heating pipes.
The first line of input contains a single integer, stating the number of floors to handle. Then
follow n floor descriptions, each beginning on a new line with two integers, 2 ≤ r ≤ 10
and 2 ≤ c ≤ 10, defining the size of the floor – r-by-c modules. Beginning on the next line
follows a floor description in ASCII format, in total 2r + 1 rows, each with 2c + 2 characters,
including the final newline. All floors are perfectly rectangular, and will always have an
even number of modules. All interior walls are represented by numeric characters, ’0’ to ’9’,
indicating the cost of routing pipes through the wall (see sample input).
For each test case, output a single line with the cost of the cheapest route.
3
4 3
#######
# 2 3 #
#1#9#1#
# 2 3 #
#1#7#1#
# 5 3 #
#1#9#1#
# 2 3 #
#######
4 4
#########
# 2 3 3 #
#1#9#1#4#
# 2 3 6 #
#1#7#1#5#
# 5 3 1 #
#1#9#1#7#
# 2 3 0 #
#########
2 2
#####
# 1 #
#2#3#
# 4 #
#####
28
45
10
Migrated from old NTUJ.
nwerc2004
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