hdu3037 Saving Beans 题意:n个不同的盒子,每个盒子里放一些球(可不放),总球数<=m,求方案数. $1<=n,m<=1e9,1<p<1e5,p∈prime$ 卢卡斯(Lucas)定理(计算组合数 防爆精度) $lucas(n,m,p)=lucas(n/p,m/p,p)*C(n\%p,m\%p,p)$ $lucas(n,0,p)=1$ 老套路,插板法. 设m个球都要放,多一个盒子轻松解决. 根据插板法得方案数$=C(n+m,n)$ 跑一遍Lucas. en…

Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) 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 c…

题目大概问小于等于m个的物品放到n个地方有几种方法. 即解这个n元一次方程的非负整数解的个数$x_1+x_2+x_3+\dots+x_n=y$,其中0<=y<=m. 这个方程的非负整数解个数是个经典问题,可以+1转化正整数解的个数用插板法解决:$C_{y+n-1}^{n-1}=C_{y+n-1}^y$. 而0<=y<=m,最后的结果就是—— $$\sum_{i=0}^m C_{i+n-1}^i$$ $$C_{n-1}^0+C_{n}^1+C_{n+1}^2+\dots+C_{n-1…

[基本解题思路] 将n个相同的元素排成一行,n个元素之间出现了(n-1)个空档,现在我们用(m-1)个“档板”插入(n-1)个空档中,就把n个元素隔成有序的m份,每个组依次按组序号分到对应位置的几个元素(可能是1个.2个.3个.4个.….),这样不同的插入办法就对应着n个相同的元素分到m组的一种分法,这种借助于这样的虚拟“档板”分配元素的方法称之为插板法. [基本题型的变形(一)] 题型:有n个相同的元素,要求分到m组中,问有多少种不同的分法? 解题思路:这种问题是允许有些组中分到的元素为“0”…

Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 4315    Accepted Submission(s): 1687 Problem Description Although winter is far away, squirrels have to work day and night to save be…

Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2079    Accepted Submission(s): 748 Problem Description Although winter is far away, squirrels have to work day and night to save bea…

hdu 3037 Saving Beans 题目大意:n个数,和不大于m的情况,结果模掉p,p保证为素数. 解题思路:隔板法,C(nn+m)多选的一块保证了n个数的和小于等于m.可是n,m非常大,所以用到Lucas定理. #include <cstdio> #include <cstring> #include <algorithm> using namespace std; typedef long long ll; ll n, m, p; ll qPow (ll a…

如果您有n+1树,文章n+1埋不足一棵树m种子,法国隔C[n+m][m] 大量的组合,以取mod使用Lucas定理: Lucas(n,m,p) = C[n%p][m%p] × Lucas(n/p,m/p,p) ; Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2314    Accepted Submissi…

Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 8258    Accepted Submission(s): 3302 Problem Description Although winter is far away, squirrels have to work day and night to save be…

Saving Beans Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 5769    Accepted Submission(s): 2316 Problem Description Although winter is far away, squirrels have to work day and night to save b…