Similarity of necklaces
Time Limit:2000MS Memory Limit:65536K
Total Submit:24 Accepted:4
Description The
story is based on a real dream of mine. The description of rules is
exactly what I dreamt. Do not start to code before you have understood
it well.
The little cat is preparing a bead necklace for his girlfriend - a
DIY one to express his affection. N (4 <= N <= 400) different
kinds of beads (wooden, plastic, glass, pearl, DIAMOND!?, etc) have
been kept in his huge casket, which are the only source of heads to
make his necklace.
By the impulse of curiosity, the little cat made two strings of
beads unthinkingly, one for him and one for his girlfriend ¨C a pair of
"lover-necklaces". Will his girlfriend like it? By the market research,
how they look like depends on the similarity factor of two necklaces. A
necklace can be considered as a linked list of M beads.
The similarity of two beads forms an N * N table. For example:
The similarity factor of two necklaces can be determined by the sum of M corresponding pair of beads. For example:
Necklace1: WPPWW
Necklace2: DPDDW
Similarly factor = Table[W,D] + Table[P,P] + Table[P,D] + Table[W,D] + Table[W,W] = -7 + 1 + 1 + (-7) + 6 = -6
Since we do not much care about what the necklace exactly is, (what
is more, the little cat wants to keep it secret until his girlfriend's
birthday) we use another N * N table to record number of existences of
different pairs:
You are given the table Pairs, but to determine the table Table.
The purpose is to make the similarity factor of two necklaces as large
as possible. There's one more restriction holds for Table, Low[i, j]
<= Table[i, j] <= Up[i, j] (an upper bound and an lower bound
given to you). Obviously Low[i, j] = Low[j, i] and Up[i, j] = Up[j, i].
Background in my dream: the little cat has special magic. At one
time, he can turn all the pearls to diamonds, and all the diamonds to
pearls. More precise speaking, he can swap two different kinds of beads
at one time. That is why N * N Pairs is fixed, but we can modify Table
ourselves!
Input The input contains a number of test cases. Each of the following blocks denotes a single test case.
A test case starts by an integer N (4 <= N <= 400) and N
lines followed. The i-th line followed contains 3 * (N ¨C i + 1)
integers, in which the j-th triple denotes Pairs[i, j + i - 1], Low[i,
j + i - 1] and Up[i, j + i - 1].
Restrictions: -10000 <= Low[i, j] < Up[i, j] <= 10000,
-100000 <= Pair[i, j] <= 100000. From the input given, you may
assume that there is always a solution.
Output For each test case, output a single line with a single number, which is the largest similarity that you can generate.
Sample Input
4
7 1 10 0 -10 10 2 -10 10 0 -10 10
0 1 10 0 -10 10 0 -10 10
0 1 10 0 -10 10
0 1 10
4
0 1 10 2 -10 10 2 -10 10 2 -10 10
0 1 10 2 -10 10 2 -10 10
0 1 10 2 -10 10
0 1 10
Sample Output
90
-4
Hint An optimum Table for the first sample case:

Source POJ Monthly--2006.01.22,Zeyuan Zhu
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