A knapsack optimizing problem

Revision en3, by tzc___wk, 2020-04-01 06:00:51

You're given $n$ integers $a_1,a_2,\dots,a_n$, you need to count the number of ways to choose some of them (no duplicate) to make the sum equal to $S$. Print the answer in modulo $10^9+7$. How to solve this problem in polynomial time?

Note: The $n,S$ can be as large as $10^5$ so using single DP can't work. Using polygon $ln$ or $exp$ might work. But I don't know how to use them (I've just heard of it). Can anyone explain it?

#### History

Revisions

Rev. Lang. By When Δ Comment
en3 tzc___wk 2020-04-01 06:00:51 197
en2 tzc___wk 2019-12-06 17:02:56 19 Tiny change: 'ual to $S$, in modulo' -> 'ual to $S$. Print the answer in modulo'
en1 tzc___wk 2019-12-06 17:01:08 246 Initial revision (published)