In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written {\displaystyle {\tbinom {n}{k}}.}…

题目传送门 Solution 应该这个做法不是很常见吧. 我们设 \(f_{i,j}\) 表示前面 \(i\) 个数,选出的数和为 \(j\) 的贡献之和.因为我们有以下式子: \[\sum_{i=a}^{b} \binom{i}{a}=\binom{b+1}{a+1} \] 所以,我们可以得到转移式: \[f_{i,j}=\sum_{k} f_{i-1,k}\times \binom{j-k+1}{a_i+1} \] 然后,我们假设设: \[F_i(x)=\sum_{j=1}^{\infty}…

\(\mathcal{Description}\)   Link.   给定非负整数序列 \(\{a_n\}\),设 \(\{b_n\}\) 是一个非负整数序列且 \(\sum_{i=1}^nb_i\le m\),求 \[\sum_{\{b_n\}}\prod_{i=1}^n\binom{b_i}{a_i}\bmod(10^9+7) \]   \(n,a_i\le2\times10^3\). \(\mathcal{Solution}\)   鉴于这是 ARC D,可以直观感受到是一个代码不长的组…

UVA - 10375 Choose and divide Choose and divide Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 4053   Accepted: 1318 Description The binomial coefficient C(m,n) is defined as m! C(m,n) = -------- n!(m-n)! Given four natural numbers p, q…

Lucas' theorem In number theory, Lucas's theorem expresses the remainder of division of the binomial coefficient by a prime number p in terms of the base p expansions of the integers m and n.     ----wiki 表达式 对于非负整数m.n和素数p,如果有: 则有下式成立: 牛刀小试 题目链接:hdu-…

Conjugate prior relationships The following diagram summarizes conjugate prior relationships for a number of common sampling distributions. Arrows point from a sampling distribution to its conjugate prior distribution. The symbol near the arrow indic…

数组的使用 package javaDemo; import java.util.*; /** * * @author Administrator * @version 1.0 * * */ public class test { public static void main(String[] args) { String[] greeting = new String[3]; greeting[0] = "Welcome to Core Java"; greeting[1] = &…

Binomial theorem One can define\[{r \choose k}=\frac{r\,(r-1) \cdots (r-k+1)}{k!} =\frac{(r)_k}{k!}\] Then, if \(x\) and \(y\) are real numbers with \(|x| > |y|\)( This is to guarantee convergence. Depending on \(r\), the series may also converge som…

质因数分解: Choose and divide Time Limit: 3000MS   Memory Limit: Unknown   64bit IO Format: %lld & %llu id=19601" class="login ui-button ui-widget ui-state-default ui-corner-all ui-button-text-only" style="display:inline-block; position…

最近做到了一些有趣的散题,于是开个Blog记录一下吧… (如果有人想做这些题的话还是不要看题解吧…) 2017-03-16 PE 202 Laserbeam 题意:有一个正三角形的镜子屋,光线从$C$点射入,求恰好反射$12017639147$次后在$C$点射出的方案数. 题解:关于反射问题容易想到对称性,不断对称翻转正三角形,可以密铺整个平面,这样一条反射$k$次的路径对应平面上经过$k$条边的路径. 然后取$CB,CA$为基,把平面画正,就能得到一个带有平行的对角线的网格图,稍微观察一下就能…