Goods transportation
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Description
There are
The
For each pair of cities
Determine the maximum number of produced goods that can be sold in total in all the cities after a sequence of transportations.
Input
The first line of the input contains two integers
The second line contains
The third line of input contains n integers
Output
Print the maximum total number of produced goods that can be sold in all cities after a sequence of transportations.
Solution
Build a network of the following form: The network will consist of
The value of the maximum flow in this network is the answer to the problem. Since the network contains
Instead, we will find a capacity of the minimal cut in this network. The cut in this case is a partition of the set of all nodes from
Capacity of the minimal cut can be found using the following dynamic programming:
The answer to the problem can be obtained as
The resulting complexity of this solution is
翻译一下就是考虑网络流:
1.
2.
3.
最大流就是答案,但直接跑是
Source
http://codeforces.com/contest/724/problem/E
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