pojPseudoprime numbers (快速幂)】的更多相关文章

Description Fermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, known as base-a ps…
POJ3641 Pseudoprime numbers p是Pseudoprime numbers的条件: p是合数,(p^a)%p=a;所以首先要进行素数判断,再快速幂. 此题是大白P122 Carmichael Number 的简化版 /* * Created: 2016年03月30日 22时32分15秒 星期三 * Author: Akrusher * */ #include <cstdio> #include <cstdlib> #include <cstring&g…
POJ1995 Raising Modulo Numbers 计算(A1B1+A2B2+ ... +AHBH)mod M. 快速幂,套模板 /* * Created: 2016年03月30日 23时01分45秒 星期三 * Author: Akrusher * */ #include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> #include <ctime> #…
Raising Modulo Numbers Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5532   Accepted: 3210 Description People are different. Some secretly read magazines full of interesting girls' pictures, others create an A-bomb in their cellar, oth…
题意:给你一个数,让你判断是否是非素数,同时a^n%n==a (其中 a 的范围为 2~n-1) 思路:先判断是不是非素数,然后利用快速幂对每个a进行判断 代码: #include <iostream> #include <cmath> #include <cstdio> #include <algorithm> #define ll long long using namespace std; bool isprime(ll num) { ) return…
ZOJ2150 快速幂,但是用递归式的好像会栈溢出. #include<cstdio> #include<cstdlib> #include<iostream> #include<cmath> using namespace std; long long M,i; #define LL long long int _work(LL a,LL n) { LL ans=1; while(n){ if(n&1){ ans=(ans*a)%M; n--; }…
Problem Description Xinlv wrote some sequences on the paper a long time ago, they might be arithmetic or geometric sequences. The numbers are not very clear now, and only the first three numbers of each sequence are recognizable. Xinlv wants to know…
题意: 思路: 对于每个幂次方,将幂指数的二进制形式表示,从右到左移位,每次底数自乘,循环内每步取模. #include <cstdio> typedef long long LL; LL Ksm(LL a, LL b, LL p) { LL ans = 1; while(b) { if(b & 1) { ans = (ans * a) % p; } a = (a * a) % p; b >>= 1; } return ans; } int main() { LL p, a…
Pseudoprime numbers Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 7954 Accepted: 3305 Description Fermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and…
题目:http://poj.org/problem?id=1995 题目解析:求(A1B1+A2B2+ ... +AHBH)mod M. 大水题. #include <iostream> #include <stdio.h> #include <string.h> #include <algorithm> #include <math.h> using namespace std; int n,mod,sum; int main() { ],b[…
#include <cstdio> typedef long long ll; int quick_pow(ll a,ll b,ll mod){ ll ans=; ))ans=(ans*a)%mod; return ans; } int main(){ int z,m,h,a,b,ans; for(scanf("%d",&z);z--;){ scanf(; while(h--)scanf("%d%d",&a,&b),ans=(an…
A sequence of numbers Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 4550    Accepted Submission(s): 1444 Problem Description Xinlv wrote some sequences on the paper a long time ago, they might…
  Carmichael Numbers  An important topic nowadays in computer science is cryptography. Some people even think that cryptography is the only important field in computer science, and that life would not matter at all without cryptography. Alvaro is one…
Raising Modulo Numbers Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5934   Accepted: 3461 Description People are different. Some secretly read magazines full of interesting girls' pictures, others create an A-bomb in their cellar, oth…
Raising Modulo Numbers Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 9512 Accepted: 5783 Description People are different. Some secretly read magazines full of interesting girls' pictures, others create an A-bomb in their cellar, others…
Count Numbers 时间限制: 8 Sec  内存限制: 128 MB提交: 43  解决: 19[提交] [状态] [讨论版] [命题人:admin] 题目描述 Now Alice wants to sum up all integers whose digit sum is exactly ab .However we all know the number of this kind of integers are unlimited. So she decides to sum u…
 C - Lucky Numbers Crawling in process... Crawling failed Time Limit:500MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u Submit Status Description The numbers of all offices in the new building of the Tax Office of IT City will have lu…
题目链接: https://projecteuler.net/problem=435 题意: The Fibonacci numbers $ {f_n, n ≥ 0}$ are defined recursively as \(f_n = f_{n-1} + f_{n-2}\) with base cases \(f_0 = 0\) and \(f_1 = 1\). Define the polynomials $ {F_n, n ≥ 0} $ as $F_n(x) =\sum_{i=0}^{n…
-->Raising Modulo Numbers Descriptions: 题目一大堆,真没什么用,大致题意 Z M H A1  B1 A2  B2 A3  B3 ......... AH  BH 有Z组数据   求(A1B1+A2B2+ ... +AHBH)mod M. Sample Input 3 16 4 2 3 3 4 4 5 5 6 36123 1 2374859 3029382 17 1 3 18132 Sample Output 2 13195 13 题目链接https://v…
-->Carmichael Numbers  Descriptions: 题目很长,基本没用,大致题意如下 给定一个数n,n是合数且对于任意的1 < a < n都有a的n次方模n等于a,这个数就是Carmichael Number. 输出The number n is a Carmichael number. n是素数 输出 n is normal. Input 多组输入,第一行给一个n (2 < n < 65000) .n = 0 表示输入结束并不需要处理 Output 对…
Fermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, known as base-a pseudoprimes,…
题目链接:POJ 3641 Description Fermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, know…
斐波那契数列后四位可以用快速幂取模(模10000)算出.前四位要用公式推 HDU 3117 Fibonacci Numbers(矩阵快速幂+公式) f(n)=(((1+√5)/2)^n+((1-√5)/2)^n)/√5 假设F[n]可以表示成 t * 10^k(t是一个小数),那么对于F[n]取对数log10,答案就为log10 t + K,此时很明显log10 t<1,于是我们去除整数部分,就得到了log10 t 再用pow(10,log10 t)我们就还原回了t.将t×1000就得到了F[n…
题意: 斐波那契数列f(0) = 0, f(1) = 1, f(n+2) = f(n+1) + f(n) (n ≥ 0) 输入a.b.n,求f(ab)%n 分析: 构造一个新数列F(i) = f(i) % n,则所求为F(ab) 如果新数列中相邻两项重复出现的话,则根据递推关系这个数列是循环的. 相邻两项所有可能组合最多就n2中,所以根据抽屉原理得到这个数列一定是循环的. 求出数列的周期,然后快速幂取模即可. #include <cstdio> #include <iostream>…
题目大意 判断一个数是否是伪素数 题解 赤果果的快速幂取模.... 代码: #include<iostream> #include<cmath> using namespace std; #define LL long long LL mul_mod(LL a,LL b,int n) { return a*b%n; } LL pow_mod(LL a,LL p,LL n) { ) ; LL ans=pow_mod(a,p/,n); ans=ans*ans%n; ==) ans=an…
题目链接:http://codeforces.com/gym/101466/problem/K 题目: 题意: 给你一棵有n个节点的树,根节点始终为0,有两种操作: 1.RAND:查询以u为根节点的子树上的所有节点的权值的乘积x,及x的因数个数. 2.SEED:将节点u的权值乘以x. 思路: 比赛时少看了因数不大于13这句话,然后本题难度增加数倍,肝了两个小时都没肝出来,对不起队友啊,今天的组队训练赛实力背锅…… 这题一眼线段树,由于是对一棵子树进行处理,因此我们采用常规套路,借助dfs序将子树…
题目描述: 请输出(3+√5)^n整数部分最后3位.如果结果不超过2位,请补足前导0. 分析: 我们最容易想到的方法肯定是直接计算这个表达式的值,但是这样的精度是不够的.朴素的算法没有办法得到答案.但是我们根据分析可以发现这个问题不用求出√5的值也可以得到答案. 我们可以发现,将(3+√5)^n这个式子展开后就是An+Bn√5的形式.同样的,我们将(3-√5)^n这个式子展开后就是An-Bn√5. 因此,(3+√5)^n+(3-√5)^n=2An是一个整数,其中0<(3-√5)^n <1,是解…
输入a和p.如果p不是素数,则若满足ap = a (mod p)输出yes,不满足或者p为素数输出no.最简单的快速幂,啥也不说了. #include<iostream> #include<cstdio> #include<cstring> #include<cmath> using namespace std; typedef long long ll; ll p,a; int whether(int p) { ; ;i*i<=p;i++) ) {…
题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=2817 解题思路:arithmetic or geometric sequences 是等差数列和等比数列的意思, 即令输入的第一个数为a(1),那么对于等差数列 a(k)=a(1)+(k-1)*d,即只需要求出 a(k)%mod   又因为考虑到k和a的范围, 所以对上式通过同余作一个变形:即求出 (a(1)%mod+(k-1)%mod*(d%mod))%mod 对于等比数列 a(k)=a(1)*q…
题目链接:http://poj.org/problem?id=1995 解题思路:用整数快速幂算法算出每一个 Ai^Bi,然后依次相加取模即可. #include<stdio.h> long long quick_mod(long long a,long long b,long long c) { long long ans=1; while(b) { if(b&1) { ans=ans*a%c; } b>>=1; a=a*a%c; } return ans; } int…