A thief made his way to a shop. As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of products of each kind. The cost of one product of kind i is ai. The t…

3992: [SDOI2015]序列统计 Time Limit: 30 Sec  Memory Limit: 128 MBSubmit: 1155  Solved: 532[Submit][Status][Discuss] Description 小C有一个集合S,里面的元素都是小于M的非负整数.他用程序编写了一个数列生成器,可以生成一个长度为N的数列,数列中的每个数都属于集合S. 小C用这个生成器生成了许多这样的数列.但是小C有一个问题需要你的帮助:给定整数x,求所有可以生成出的,且满足数列中…

题目 Source http://codeforces.com/contest/632/problem/E Description A thief made his way to a shop. As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of pro…

传送门 生成函数简单题. 题意:给出一个集合A={a1,a2,...as}A=\{a_1,a_2,...a_s\}A={a1​,a2​,...as​},所有数都在[0,m−1][0,m-1][0,m−1]之间,mmm是一个质数,求满足全部由这个集合里的组成且长度为nnn且所有数之积与xxx在模mmm意义下相同的数列总数. 思路:对a1,a2,..,as,xa_1,a_2,..,a_s,xa1​,a2​,..,as​,x全部化成gb1,gb2,...gbs,gyg^{b_1},g^{b_2},..…

E. Thief in a Shop   A thief made his way to a shop. As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of products of each kind. The cost of one product o…

还是没有理解透原根--题目提示其实挺明显的,M是质数,然后1<=x<=M-1 这种计数就容易想到生成函数,但是生成函数是加法,而这里是乘法,所以要想办法变成加法 首先因为0和任何数乘都是0,和其他数规则不相符,所以不考虑(答案也没让求) 然后看原根的性质,设g是M的原根,那么\( g^i%M 0<=i<M-1 \)就是1~M-1的不重集合,所以可以把乘法变成原根指数的加法,这样就变成多项式乘法了,可以用NTT优化 然后n非常大,所以使用快速幂进行多项式乘法 #include<…

思路: 普通的DP很好想吧 f[i][j]+=f[i-1][j*s[k]]  前i个数  mod m=j 的个数 m是质数  模数是质数  这就很有趣了 那么我们就求出来原根  所有的数都取指数 搞出生成函数乘法就变成了加法 快速幂+$NTT$就好了 (注意特判零) //By SiriusRen #include <cstdio> #include <cstring> #include <algorithm> using namespace std; #define i…

A thief made his way to a shop. As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of products of each kind. The cost of one product of kind i is ai. The t…

All bus tickets in Berland have their numbers. A number consists of n digits (n is even). Only k decimal digits d1,d2,…,dk can be used to form ticket numbers. If 0 is among these digits, then numbers may have leading zeroes. For example, if n=4 and o…

题目:https://www.lydsy.com/JudgeOnline/problem.php?id=3992 有转移次数.模M余数.方案数三个值,一看就是系数的地方放一个值.指数的地方放一个值.做卷积的次数表示一个值(应该是表示转移次数). 可以余数和方案数都要求相乘,指数只能相加,怎么办? 然后看题解,原来可以用M的原根的幂来表示余数那个信息!因为原根的几次幂和%M剩余类可以一一对应(除了%M==0!!!),所以用原根的幂表示%M余几,两个余数相乘就变成原根的指数相加了!把该余数对应的原根…