# 标签存档: SGU104

## SGU 104 解题报告

http://acm.sgu.ru/problem.php?contest=0&problem=104

## 104. Little shop of flowers

time limit per test: 0.50 sec.
memory limit per test: 4096 KB

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 花瓶 1 2 3 4 5 Bunches 花束 1 (azaleas 杜鹃花) 7 23 -5 -24 16 2 (begonias 秋海棠) 5 21 -4 10 23 3 (carnations 康乃馨) -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.
• FV ≤ 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.
• 1 ≤ F ≤ 100 表示花的种数。
• FV ≤ 100 表示花瓶数。
• -50 Aij 50 表示i号花束放入j号花瓶产生的美学价值。

### Input

• 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 thej th number on the (j+1) st line of the input file.
• 第一行: F, V.
• 接下来F行每行V个数，其中Aij第(i+1) 行j 列 。

### Output

• 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.
• 第一行包括一个整数表示最大美学价值。
• 第二行从左到右F个数表示最优方案的每个花束放在哪一个花瓶里，数据用空格隔开。