HDU3037(Lucas定理)
来源:互联网 发布:js 取反运算符 编辑:程序博客网 时间:2024/06/08 04:19
Saving Beans
Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3542 Accepted Submission(s): 1354
Problem Description
Although winter is far away, squirrels have to work day and night to save beans. They need plenty of food to get through those long cold days. After some time the squirrel family thinks that they have to solve a problem. They suppose that they will save beans in n different trees. However, since the food is not sufficient nowadays, they will get no more than m beans. They want to know that how many ways there are to save no more than m beans (they are the same) in n trees.
Now they turn to you for help, you should give them the answer. The result may be extremely huge; you should output the result modulo p, because squirrels can’t recognize large numbers.
Input
The first line contains one integer T, means the number of cases.
Then followed T lines, each line contains three integers n, m, p, means that squirrels will save no more than m same beans in n different trees, 1 <= n, m <= 1000000000, 1 < p < 100000 and p is guaranteed to be a prime.
Output
You should output the answer modulo p.
Sample Input
2
1 2 5
2 1 5
Sample Output
3
3
Hint
Hint
For sample 1, squirrels will put no more than 2 beans in one tree. Since trees are different, we can label them as 1, 2 … and so on.
The 3 ways are: put no beans, put 1 bean in tree 1 and put 2 beans in tree 1. For sample 2, the 3 ways are:
put no beans, put 1 bean in tree 1 and put 1 bean in tree 2.
Source
2009 Multi-University Training Contest 13 - Host by HIT
Recommend
gaojie | We have carefully selected several similar problems for you: 3033 3038 3036 3035 3034
公式是C(n+m,m)用Lucas定理就过了
#include "cstring"#include "iostream"#include "string.h"#include "cstdio"using namespace std;typedef long long LL;const int INF = 0x3f3f3f3f;const int maxn = 100005;LL fact[maxn];LL p;LL quick_pow(LL a, LL k){ LL ans = 1; while(k) { if(k & 1) (ans *= a) %= p; (a *=a) %= p; k >>= 1; } return ans;}void Init(){ fact[0] = 1; for(int i = 1; i <= p; i ++) { fact[i] = fact[i - 1] * i % p; }}LL Inv(LL n){ return quick_pow(n, p - 2);}LL C(LL n, LL m){ if(n < m) return 0; return fact[n] * Inv(fact[n - m] * fact[m] % p) % p;}LL lucas(LL n, LL m){ if(m == 0) return 1; return C(n % p, m % p) * lucas(n / p, m / p) % p;}int main(){ int T; LL n, m; scanf("%d", &T); while(T--) { scanf("%lld%lld%lld", &n, &m, &p); Init(); printf("%lld\n", lucas(n+m, m)); } return 0;}
- HDU3037(Lucas定理)
- lucas定理(hdu3037,)
- 数论 Lucas定理 hdu3037
- hdu3037 LUCAS定理运用。
- Lucas定理&&hdu3037
- 【hdu3037】【Lucas定理】Saving Beans
- hdu3037 lucas 定理 组合数取模
- Hdu3037 Saving Beans Lucas定理
- hdu3037 组合数 lucas定理
- hdu3037 Saving Beans (lucas定理+组合数公式)
- [HDU3037]Saving Beans(组合数学Lucas定理)
- hdu3037 大组合数取模(Lucas定理)
- HDU3037(Lucas定理求大组合数取模)
- hdu3037 Saving Beans(Lucas定理+费马小定理or扩展欧几里德算发)
- HDU3037——Saving Beans(数论,组合数取模,lucas定理模板)
- 【日常学习】【组合数取模Lucas定理】HDU3037 Saving Beans题解
- hdu3037 隔板法+Lucas定理求大组合取模
- Lucas模板 hdu3037
- Android 通过系统使用NotificationListenerService 监听各种Notification的使用方法
- HDU 2108 Shape of HDU
- object-c property关键字
- adt怎么关联第三方jar包源码的方法
- 拥抱高效、拥抱 Bugtags 之来自用户的声音(五)
- HDU3037(Lucas定理)
- Git 合并 patch 时的冲突处理一例
- PHP数据库连接池SQL Relay安装使用
- UVa 12186 Another Crisis dp:树上dp
- Wireshark 文件分割和合并
- 后台为php的apns证书
- Android深入浅出系列之广播机制—2-Android中的广播机制
- Unity3D 优化之路(一):DrawCall
- Android ADB命令