chore(CPlusPlus): add segmented sieve for range (#535)

Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>

algorithms/CPlusPlus/Maths/segmented-sieve-range.cpp

@@ -0,0 +1,84 @@
+/*
+Problem: finding all prime numbers in a range [L,R], where R <= 1e12 and (R-L+1) <= 1e7.
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+//function to find prime numbers between L and R
+void segmented_sieve_range(long int L, long int R){
+
+    // generate all primes up to sqrt(R)
+    long int e = sqrt(R);
+
+    // vector to store whether ith element is visited or not
+    vector<bool> check(e + 1, false);
+
+    //stores all primes till sqrt(R)
+    vector<long int> primes;
+    
+    for (long int i = 2; i <= e; ++i) {
+        if (!check[i]) {
+
+            //i is a prime number
+            primes.push_back(i);
+            for (long int j = i*i; j <= e; j += i){
+                check[j] = true;
+            }
+        }
+    }
+
+    vector<bool> isPrime(R - L + 1, true);
+
+    //edge case
+    if(L == 1){
+        isPrime[0] = false;
+    }
+
+    for (long int i = 0; i < primes.size() ; i++){
+
+        //current Prime
+        long int cur = primes[i];
+        long int product = cur*cur;
+
+        for(long int start = max(product, (L + cur -1)/product); start <= R ; start += cur){
+            isPrime[start - L] = false;
+        }
+    }
+
+
+    //Printing all primes in the range L to R 
+    for(long int i = 0; i < isPrime.size(); i++){
+        if(isPrime[i]){
+            //current index element is a prime number
+            cout<< L + i << " ";
+        }
+    } 
+
+    cout << endl;
+}
+
+//main starts
+int main()
+{
+    long int L, R;
+    cin >> L >> R;
+
+    segmented_sieve_range(L, R);
+
+    return 0;
+}
+
+/*
+Time Complexity - O((R−L+1)log(R) + √R)
+
+Input: 
+30 50
+Output:
+31 37 41 43 47
+
+Input: 
+10 20
+Output: 
+11 13 17 19
+*/

algorithms/CPlusPlus/README.md

@@ -140,6 +140,7 @@
 - [Missing number](Maths/missing-number.cpp)
 - [Factorial of a number](Maths/factorial.cpp)
 - [Prime-number](Maths/prime-number.cpp)
+- [Segmented Sieve](Maths/segmented-sieve-range.cpp)
 
 # Recursion