LITTLE SHOP OF FLOWERS
PROBLEM
You want to arrange the window of your flower shop in a most pleasant way. You have F bunches of flowers, each
being of a different kind, and at least as many vases ordered in a row. The vases are glued onto the shelf and are
numbered consecutively 1 through V, where V is the number of vases, from left to right so that the vase 1 is the
leftmost, and the vase V is the rightmost vase. The bunches are moveable and are uniquely identified by integers
between 1 and F. These id-numbers have a significance: They determine the required order of appearance of the
flower bunches in the row of vases so that the bunch i must be in a vase to the left of the vase containing
bunch j whenever i < j. Suppose, for example, you have bunch of azaleas (id-number=1), a bunch of begonias (id-
number=2) and a bunch of carnations (id-number=3). Now, all the bunches must be put into the vases keeping their
id-numbers in order. The bunch of azaleas must be in a vase to the left of begonias, and the bunch of begonias must
be in a vase to the left of carnations. If there are more vases than bunches of flowers then the excess will be left
empty. A vase can hold only one bunch of flowers.
Each vase has a distinct characteristic (just like flowers do). Hence, putting a bunch of flowers in a vase results in a
certain aesthetic value, expressed by an integer. The aesthetic values are presented in a table as shown below.
Leaving a vase empty has an aesthetic value of 0.

V A S E S
1
2
3
4
5
Bunches
1 (Azaleas)
7
23
-5
-24
16
2 (Begonias)
5
21
-4
10
23
3 (Carnations)
-21
5
-4
-20
20
According to the table, azaleas, for example, would look great in vase 2, but they would look awful in vase 4.
To achieve the most pleasant effect you have to maximize the sum of aesthetic values for the arrangement while
keeping the required ordering of the flowers. If more than one arrangement has the maximal sum value, any one of
them will be acceptable. You have to produce exactly one arrangement.
ASSUMPTIONS
•
1 <= F <= 100 where F is the number of the bunches of flowers. The bunches are numbered 1 through F.
•
F <= V <= 100 where V is the number of vases.
•
-50 <= Aij <= 50 where Aij is the aesthetic value obtained by putting the flower bunch i into the vase j.

EXAMPLE

flower.inp:
3 5
7 23 -5 -24 16
5 21 -4 10 23
-21 5 -4 -20 20

flower.out:
53
2 4 5
EVALUATION
Your program will be allowed to run 2 seconds.
No partial credit can be obtained for a test case.

The input is a text file named flower.inp.
•
The first line contains two numbers: F, V.
•
The following F lines: Each of these lines contains V integers, so that Aij is given as the jth number on the
(i+1)st line of the input file.

The output must be a text file named flower.out consisting of two lines:
•
The first line will contain the sum of aesthetic values for your arrangement.
•
The second line must present the arrangement as a list of F numbers, so that the k’th number on this line
identifies the vase in which the bunch k is put.

생성자가 기록되지 않았습니다.

출처 IOI 1999