Can anyone please provide any hint for this problem? Throwing Dice
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Rayan Programming Contest 2024 - Selection (Codeforces Round, Div. 1 + Div. 2)
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
Соревнования по программированию 2.0
Время на сервере: 25.11.2024 20:09:48 (i1).
Десктопная версия, переключиться на мобильную.
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Let f(n) be the number of ways of throwing dices to get a sum of n, Then consider the last dice throw. It has 6 possibilities 1-6. So f(n) = f(n-1) + f(n-2) + ... + f(n-6).
The recurrence is correct. However, unfortunately, it TLE's. There is hope though. This is a linear recurrence can be computed for arbitrary values of n using fast matrix exponentiation. Here is a geeks for geeks article that illustrates the technique in action https://www.geeksforgeeks.org/find-nth-term-a-matrix-exponentiation-example/
My fav trick in such problems:
1. precalc first 20 values
2. use Berlekamp-Massey algorihm to compute n_th value of Linear recurrence
source: https://mirror.codeforces.com/blog/entry/61306?
another problems:
https://mirror.codeforces.com/contest/392/submission/51596991
https://mirror.codeforces.com/contest/678/submission/51597127