中国剩余定理也称孙子定理,是中国古代求解一次同余式组(见同余)的方法.是数论中一个重要定理. 这玩意在luogu居然有模板题: [TJOI2009]猜数字 先来看一个问题: 在<孙子算经>中有这样一个问题:"今有物不知其数,三三数之剩二(除以3余2),五五数之剩三(除以5余3),七七数之剩二(除以7余2),问物几何?" 熟悉吗小学数学学过吗 这样的问题是基本的中国剩余定理的运用,解题过程有三步: 找出三个数:从\(3\)和\(5\)的公倍数中找出被\(7\)除余\(1\)的…

Biorhythms Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 117973   Accepted: 37026 Description Some people believe that there are three cycles in a person's life that start the day he or she is born. These three cycles are the physical,…

Biorhythms Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 117973   Accepted: 37026 Description Some people believe that there are three cycles in a person's life that start the day he or she is born. These three cycles are the physical,…

Bell Time Limit:3000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u Submit Status Practice HDU 4767   Description What? MMM is learning Combinatorics!? Looks like she is playing with the bell sequence now: bell[n] = number of ways to pa…

二进制枚举+容斥原理+中国剩余定理 #include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #include<cmath> using namespace std; #define MAXN 20 typedef long long LL; int n; int s[MAXN]; LL a[MAXN], m[MAXN]; //a是余数,m是除数 LL ex…

我理解的中国剩余定理的含义是:给定一个数除以一系列互素的数${p_1}, \cdots ,{p_n}$的余数,那么这个数除以这组素数之积($N = {p_1} \times  \cdots  \times {p_n}$)的余数也确定了,反之亦然. 用表达式表示如下: \[\begin{array}{l}x \equiv {a_1}(\bmod {p_1})\\{\rm{     }} \vdots \\x \equiv {a_n}(\bmod {p_n})\end{array}\] 那么任何满足…

题目链接: http://www.51nod.com/onlineJudge/user.html#!userId=21687 题意: 中文题诶~ 思路: 本题就是个中国剩余定理模板题,不过模拟也可以过,而且时间复杂度嘛~ 我们可以知道gcd得出两个数的最大公约在最坏的情况下(a, b是相邻的两个斐波拉契数)是O(logn)的, 同理可以知道exgcd也是O(lgn)时间复杂度,因此中国剩余定理时间复杂度是O(nlogn); 而模拟的话最坏的情况下需要O(n*x)的时间~本题两种算法都是15ms.…

Unknown Treasure Time Limit: 1500/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 2389    Accepted Submission(s): 885 Problem Description On the way to the next secret treasure hiding place, the mathematician…

/* 中国剩余定理可以描述为: 若某数x分别被d1..….dn除得的余数为r1.r2.….rn,则可表示为下式: x=R1r1+R2r2+…+Rnrn+RD 其中R1是d2.d3.….dn的公倍数,而且被d1除,余数为1:(称为R1相对于d1的数论倒数) R1 . R2 . … . Rn是d1.d2.….dn-1的公倍数,而且被dn除,余数为1: D是d1.d2.….的最小公倍数: R是任意整数(代表倍数),可根据实际需要决定: 且d1..….必须互质,以保证每个Ri(i=1,2,…,n)都能求…

Biorhythms Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 110991   Accepted: 34541 Description Some people believe that there are three cycles in a person's life that start the day he or she is born. These three cycles are the physical,…