Given an array A has N integer (1 <= a[i] <= 100, N <= 100) and a number X (X <= 10^9)
Counting number of ways that can get X from a subsequences of A (an element can be used as many as you want)
anyone has a idea for it ?
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
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Время на сервере: 25.11.2024 22:48:30 (h1).
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What do you mean by getting? Is it appending or sum?
it's sum
Even though X is really big, it doesn't really matter because N can be maximum 100, and every element can be maximum 100; therefore, maximum sum can be 10000. Can't we just do a simple dp?
an element can be used as many time as you want
So if A = {2,1}, X = 4, so ways are : {2, 2} {2,1,1} {1,1,1,1} etc..
Ok, I see.
An element can be used as many as you want, so maximum sum isn't 10^4. You can't do a simple dp here.
Looks pretty straight-forward. Let dx be the answer for x. If you know dx, dx + 1, ..., dx + 99, then
, so it is a linear combination of dx, dx + 1, ..., dx + 99. Which means that transition from dx, dx + 1, ..., dx + 99 to dx + 1, ..., dx + 100 can be done by matrix multiplication, and the whole problem can be solved by taking a power of this matrix (with complexity max(a[i])^3 * log(X)).