Improved Sieve in O(n) time

Author: coderick14

improvedSieve.cpp

@@ -0,0 +1,35 @@
+//Given N, find all primes less than N in O(N) time
+#include <bits/stdc++.h>
+#define ll long long
+#define MAX_SIZE 100001
+using namespace std;
+
+vector<ll> prime;   //to store the primes
+vector<bool> isPrime(MAX_SIZE, true);
+vector<ll> SPF(MAX_SIZE);   //SPF[i] stores smallest prime factor of i
+
+void improvedSieve(ll n) {
+    ll i,j;
+    isPrime[0] = isPrime[1] = false;
+    for(i=2;i<n;i++) {
+        if(isPrime[i]) {
+            prime.push_back(i);
+            SPF[i] = i; //since smallest prime factor of a prime is the prime itself
+        }
+        for(j=0;j<prime.size() && i*prime[j]<n && prime[j]<=SPF[i]; j++) {
+            isPrime[i*prime[j]] = false;
+            SPF[i*prime[j]] = prime[j];
+        }
+    }
+}
+
+int main() {
+    ll n;
+    cin>>n;
+    improvedSieve(n);
+    for(ll i=0;i<prime.size();i++ ) {
+        cout<<prime[i]<<" ";
+    }
+    cout<<endl;
+    return 0;
+}