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Improved Sieve in O(n) time

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	`1`	`+//Given N, find all primes less than N in O(N) time`
	`2`	`+#include <bits/stdc++.h>`
	`3`	`+#define ll long long`
	`4`	`+#define MAX_SIZE 100001`
	`5`	`+using namespace std;`
	`6`	`+`
	`7`	`+vector<ll> prime; //to store the primes`
	`8`	`+vector<bool> isPrime(MAX_SIZE, true);`
	`9`	`+vector<ll> SPF(MAX_SIZE); //SPF[i] stores smallest prime factor of i`
	`10`	`+`
	`11`	`+void improvedSieve(ll n) {`
	`12`	`+ ll i,j;`
	`13`	`+ isPrime[0] = isPrime[1] = false;`
	`14`	`+ for(i=2;i<n;i++) {`
	`15`	`+ if(isPrime[i]) {`
	`16`	`+ prime.push_back(i);`
	`17`	`+ SPF[i] = i; //since smallest prime factor of a prime is the prime itself`
	`18`	`+ }`
	`19`	`+ for(j=0;j<prime.size() && i*prime[j]<n && prime[j]<=SPF[i]; j++) {`
	`20`	`+ isPrime[i*prime[j]] = false;`
	`21`	`+ SPF[i*prime[j]] = prime[j];`
	`22`	`+ }`
	`23`	`+ }`
	`24`	`+}`
	`25`	`+`
	`26`	`+int main() {`
	`27`	`+ ll n;`
	`28`	`+ cin>>n;`
	`29`	`+ improvedSieve(n);`
	`30`	`+ for(ll i=0;i<prime.size();i++ ) {`
	`31`	`+ cout<<prime[i]<<" ";`
	`32`	`+ }`
	`33`	`+ cout<<endl;`
	`34`	`+ return 0;`
	`35`	`+}`

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