SPOJ Problem Set (classical)
119. Servers
Problem code: SERVERS
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The Kingdom of Byteland decided to develop a large computer network of servers
offering various services.
The network is built of n servers connected by bidirectional wires. Two servers
can be directly connected by at most one wire. Each server can be directly
connected to at most 10 other servers and every two servers are connected with
some path in the network. Each wire has a fixed positive data transmission time
measured in milliseconds. The distance (in milliseconds) D(V, W) between two
servers V and W is defined as the length of the shortest (transmission
time-wise) path connecting V and W in the network. For convenience we let D(V,
V) = 0 for all V.
Some servers offer more services than others. Therefore each server V is marked
with a natural number r(V), called a rank. The bigger the rank the more
powerful a server is.
At each server, data about nearby servers should be stored. However, not all
servers are interesting. The data about distant servers with low ranks do not
have to be stored. More specifically, a server W is interesting for a server V
if for every server U such that D(V, U) <= D(V, W) we have r(U) <= r(W).
For example, all servers of the maximal rank are interesting to all servers. If
a server V has the maximal rank, then exactly the servers of the maximal rank
are interesting for V . Let B(V) denote the set of servers interesting for a
server V.
We want to compute the total amount of data about servers that need to be
stored in the network being the total sum of sizes of all sets B(V). The
Kingdom of Byteland wanted the data to be quite small so it built the network
in such a way that this sum does not exceed 30*n.
Task
Write a program that:
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reads the description of a server network from the standard input,
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computes the total amount of data about servers that need to be stored in the
network,
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writes the result to the standard output.
Input
The input begins with the integer z, the number of test cases. Then z test
cases follow.
For each test case, in the first line there are two natural numbers n, m, where
n is the number of servers in the network (1 <= n <= 30000) and m is the
number of wires (1 <= m <= 5n). The numbers are separated by single
space.
In the next n lines the ranks of the servers are given. Line i contains one
integer ri (1 <= ri <= 10) - the rank of i-th server.
In the following m lines the wires are described. Each wire is described by
three numbers a, b, t (1 <= t <= 1000, 1 <= a, b <= n,
a <> b), where a and b are numbers of the servers connected by the
wire and t is the transmission time of the wire in milliseconds.
Output
For each test case the output consists of a single integer equal to the total
amount of data about servers that need to be stored in the network.
Example
Sample input:
1
4 3
2
3
1
1
1 4 30
2 3 20
3 4 20
Sample output:
9
(because B(1) = {1, 2}, B(2) = {2}, B(3) = {2, 3}, B(4) = {1, 2, 3, 4})
Warning: large Input/Output data, be careful with certain languages
| Added by: | Adrian Kosowski |
| Date: | 2004-07-07 |
| Time limit: | 12s
|
| Source limit: | 50000B |
| Languages: | All except: PERL 6 |
| Resource: | ACM Central European Programming Contest, Warsaw 2002 |
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