## Problem

Given an integer N, generate all primes less than or equal to N.

## Sieve of Eratosthenes - Explanation

Sieve of Eratosthenes is an algorithm that generates all prime up to N. Read this article written by +Jane Alam Jan on Generating Primes - LightOJ Tutorial. The pdf contains almost all the optimizations of Sieve of Eratosthenes.

## Code

vector<int> prime; /*Stores generated primes*/ char sieve[SIZE]; /*0 means prime*/ void primeSieve ( int n ) { sieve[0] = sieve[1] = 1; /*0 and 1 are not prime*/ prime.push_back(2); /*Only Even Prime*/ for ( int i = 4; i <= n; i += 2 ) sieve[i] = 1; /*Remove multiples of 2*/ int sqrtn = sqrt ( n ); for ( int i = 3; i <= sqrtn; i += 2 ) { if ( sieve[i] == 0 ) { for ( int j = i * i; j <= n; j += 2 * i ) sieve[j] = 1; } } for ( int i = 3; i <= n; i += 2 ) if ( sieve[i] == 0 ) prime.push_back(i); }Some lines from the code above can be omitted depending on situation. But as a whole, the above code gives us two products, a vector<int> prime which contains all generated primes and a char[] sieve that indicates whether a particular value is prime or not. We will need sieve array for optimizations in other algorithms.

## Complexity

The algorithm has runtime complexity of $O(N log (logN ) )$

vaiya segmented sieve er upor ekta tutorial likhen please. . .

ReplyDeleteOkey :) Next post will be on Segmented Sieve.

Delete:) thank you

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