pku 3422 最大费用流

最新推荐文章于 2018-07-25 09:56:01 发布

阅读量601

点赞数

CC 4.0 BY-SA版权

文章标签： matrix each numbers output input

本文链接：https://blog.youkuaiyun.com/ywhorizen/article/details/6730874

本文讨论了在给定矩阵中，从左上角到右下角的路径中，通过特定移动规则，如何最大化路径上数字的累加和，并在经过K次移动后达到的最大和。涉及算法设计和路径优化。

Kaka's Matrix Travels

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 4717		Accepted: 1834

Description

On an N × N chessboard with a non-negative number in each grid, Kaka starts his matrix travels with SUM = 0. For each travel, Kaka moves one rook from the left-upper grid to the right-bottom one, taking care that the rook moves only to the right or down. Kaka adds the number to SUM in each grid the rook visited, and replaces it with zero. It is not difficult to know the maximum SUM Kaka can obtain for his first travel. Now Kaka is wondering what is the maximum SUM he can obtain after his Kth travel. Note the SUM is accumulative during the K travels.

Input

The first line contains two integers N and K (1 ≤ N ≤ 50, 0 ≤ K ≤ 10) described above. The following N lines represents the matrix. You can assume the numbers in the matrix are no more than 1000.

Output

The maximum SUM Kaka can obtain after his Kth travel.

Sample Input

3 2
1 2 3
0 2 1
1 4 2

Sample Output

Source

POJ Monthly--2007.10.06 , Huang, Jinsong

一个矩阵，一个人只能往下或右走一格，一次从左上角走到右下角所得的价值是走过的格子的权值和，走过后这个格子中的权值边为0。现在走k次，问你能得到的最大价值？

对于每个格子拆点，设为 u , u' 则连两条边 u--->u' 容量为1，费用为权值和 u----->u' ，容量为k-1,费用为0。然后再根据能走的方向向下、右连边。最后求最大费用流（和最小费用流不同的是，这里求的是最长路（开始的时候不会出现正圈））