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algorithms/CPlusPlus/Maths/linear-sieve.cpp

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+//Linear Sieve
+//Finding primes in linear time
+
+//Every composite q must have atleast 1 prime factor
+//Let the smallest prime factor be p
+//We can say q = p*(i)
+
+//When we loop for every i, all primes not exceeding i is already stored in primes
+//We can pick out each composite exactly once by looping and breaking out when the element divides i
+
+#include<bits/stdc++.h>
+using namespace std;
+
+vector<int> primes;
+bool check[INT_MAX];
+
+
+void LinearSieve(int n) {
+    fill(check, check+n, false);    
+    for(int i=2;i<n;i++){
+        if(!check[i]) primes.push_back(i);
+        for(int j=0;j<primes.size() && i*primes[j] < n;j++){ //Executed only once for each composite
+            check[i*primes[j]] = true;
+            if(i%primes[j]==0) break; //Breaks when p divides i
+        }
+    }                             
+}
+int main() {
+    int n;
+    cin >> n;
+    LinearSieve(n); //Call the function
+    return 0;     //Time complexity : O(n*log(log(n))), Auxiliary Space: O(1)
+    //Example : n=10 , Output: 2 3 5 7   
+}