斜率优化DP入门(填坑)

最新推荐文章于 2024-02-06 11:44:45 发布

Karshilov

最新推荐文章于 2024-02-06 11:44:45 发布

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分类专栏： ACM 动态规划文章标签： DP

本文链接：https://blog.youkuaiyun.com/qq_37666409/article/details/79312788

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斜率优化作为一种优化DP的方式，目的在于将某类具有单调性的DP方程从O(n^2)优化到O(n)

可以进行斜率优化的方程一般有如下几个特征，假设当前位为i，那么有一个和i,j同时有关的元素f(i, j)，有一个仅与可继承状态j有关的g(j)，可能还有一个常量x

很抽象对不对……所以这里有一道例题（真·例题）：hdu3507Print Article

Print Article

Time Limit: 9000/3000 MS (Java/Others) Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 15344 Accepted Submission(s): 4766

Problem Description

Zero has an old printer that doesn't work well sometimes. As it is antique, he still like to use it to print articles. But it is too old to work for a long time and it will certainly wear and tear, so Zero use a cost to evaluate this degree.
One day Zero want to print an article which has N words, and each word i has a cost Ci to be printed. Also, Zero know that print k words in one line will cost

M is a const number.
Now Zero want to know the minimum cost in order to arrange the article perfectly.

Input

There are many test cases. For each test case, There are two numbers N and M in the first line (0 ≤ n ≤ 500000, 0 ≤ M ≤ 1000). Then, there are N numbers in the next 2 to N + 1 lines. Input are terminated by EOF.

Output

A single number, meaning the mininum cost to print the article.

Sample Input