Sieve of Eratosthenes (素数筛选算法) Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. For example, if n is 10, the output should be “2, 3, 5, 7″. If n is 20, the output should be “2, 3, 5, 7, 11, 13,…

寻找比n小的所有质数的方法. 2是质数, 2*i都是质数,同样3是质数,3*i也都是质数 代码如下 int n; vector<, true); prime[] = prime[] = false; ; i<=n; ++i) if (prime[i]) if (i * 1ll * i <= n) for (int j=i*i; j<=n; j+=i) prime[j] = false;…

Programming 1.3 In this problem, you'll be asked to find all the prime numbers from 1 to 1000. Prime numbers are used in allkinds of circumstances, particularly in fields such as cryptography, hashing among many others. Any method w ill be sufficient…

埃拉托色尼筛法(Sieve of Eratosthenes)是一种用来求所有小于N的素数的方法.从建立一个整数2~N的表着手,寻找i? 的整数,编程实现此算法,并讨论运算时间. 由于是通过删除来实现,而1和0则不是素数,所以从2,3,5以及其倍数删除. 用Data[]来储存所有的数,将替换好的数字存在Data[]当中 而只需做出将2,3,5以及能将这些数整除的数字替换为零:if(Data[j] % i == 0 ) Data[j]==0; 实现的代码段为: for (i = 2; i < n;…

拖了有段时间,今天来总结下两个常用的素数筛法: 1.sieve of Eratosthenes[埃氏筛法] 这是最简单朴素的素数筛法了,根据wikipedia,时间复杂度为 ,空间复杂度为O(n). 算法思想:先假定所有的数都是素数,然后从最小的素数2出发,把素数的所有倍数筛出去.又因为一个数的质因数都是成对出现的,比如100 = 1*100 = 2*50 = .....= 10*10,所以筛素数时只用筛到 n的开平方就行了. 伪代码如下: 对于任意的范围n, 设bool prime[ ],初始…

上代码. #include<cstdio> #include<cstdlib> #include<cstring> #define reg register const int MAXN=100000; bool tf[MAXN+10]; int cnt=0; void work(){ memset(tf,1,sizeof(tf));tf[1]=0; for(reg int i=2;i<=MAXN;++i){ ++cnt; if(!tf[i]) continue;…

题目描述 题目来源于 LeetCode 204.计数质数,简单来讲就是求"不超过整数 n 的所有素数个数". 常规思路 一般来讲,我们会先写一个判断 a 是否为素数的 isPrim(int a) 函数: bool isPrim(int a){ for (int i = 2; i < a; i++) if (a % i == 0)//存在其它整数因子 return false; return true; } 然后我们会写一个 countIsPrim(int n) 来计算不超过 n…

Given a number N, the output should be the all the prime numbers which is less than N. The solution is calledSieve of Eratosthenes: First of all, we assume all the number from 2 to N are prime number (0 & 1 is not Prime number). According to the Prim…

原题 原题链接 Description: Count the number of prime numbers less than a non-negative number, n. 计算小于非负数n的素数个数. 思路 这题用埃拉托斯特尼筛法来做效果比较好,普通的方法基本会TLE.但是在用了埃拉托斯特尼筛法之后,还有一些细节值得注意: (1)首先我们该用 i*i<=n 替代 i<=sqrt(n) 来避免使用 sqrt() ,因为sqrt()的操作是比较expensive的. (2)当要表示两个状…

QUESTION : What are the 10 algorithms one must know in order to solve most algorithm challenges/puzzles? ANSWER: Dynamic Programming (DP) appears to account for a plurality (some estimate up to a third) of contest problems. Of course, DP is also not…