hi how to solve the problem change from the spoj (http://www.spoj.com/problems/TPC07/)
i read concrete mathematics chapter 7 about coin change. but i can't able to understand can anybody help me to get idea about solving this problem ?
→ Обратите внимание
→ Лидеры (рейтинг)
| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | Benq | 3792 |
| 2 | VivaciousAubergine | 3647 |
| 3 | Kevin114514 | 3603 |
| 4 | jiangly | 3583 |
| 5 | turmax | 3559 |
| 6 | tourist | 3541 |
| 7 | strapple | 3515 |
| 8 | ksun48 | 3461 |
| 9 | dXqwq | 3436 |
| 10 | Otomachi_Una | 3413 |
| Страны | Города | Организации | Всё → |
→ Лидеры (вклад)
| № | Пользователь | Вклад |
|---|---|---|
| 1 | Qingyu | 157 |
| 2 | adamant | 153 |
| 3 | Um_nik | 147 |
| 3 | Proof_by_QED | 147 |
| 5 | Dominater069 | 145 |
| 6 | errorgorn | 142 |
| 7 | cry | 139 |
| 8 | YuukiS | 135 |
| 9 | TheScrasse | 134 |
| 10 | chromate00 | 133 |
→ Найти пользователя
→ Прямой эфир
Codeforces (c) Copyright 2010-2026 Михаил Мирзаянов
Соревнования по программированию 2.0
Время на сервере: 17.04.2026 12:59:12 (g2).
Десктопная версия, переключиться на мобильную.
При поддержке
This is a dynamic programming problem. First learn something about it, then approach this problem
The upper limit of n is quite large, where 1 ≤ n ≤ 1000000000. How to cater for this with DP?
Probably there is a more general formula?
Well the idea is for dp, but you need to use matrices to run it fast, in time
(50 is the maximal value of a coin).
I can explain more if you want.
It can be solved in O(1).
We want to count the number of solutions of x1 + 5x2 + 10x3 + 25x4 + 50x5 = N.
x1 must be congruent with n%5, so is equivalent to count the number of solutions of x1 + x2 + 2x3 + 5x4 + 10x5 = ⌊ N / 5⌋ = M
Let's suppose
(i.e xi = 5ai + ri), for i ≤ 3.
We can brute force all possibilities of ri, now we have to count the solutions of
a1 + a2 + 2a3 + x4 + 2x5 = ⌊ (M - r1 - r2 - 2r3) / 5⌋ = P
Grouping, (a1 + a2 + x4) + 2(a3 + x5) = P which can be solved by