Add Segmented Sieve

Number Theory/Segmented Sieve.cpp

@@ -0,0 +1,79 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+const int S = 10000;
+
+// Count primes up to n
+int count_primes(int n) {
+    vector<int> primes;
+    int nsqrt = sqrt(n);
+    vector<char> is_prime(nsqrt + 2, true);
+    for (int i = 2; i <= nsqrt; i++) {
+        if (is_prime[i]) {
+            primes.push_back(i);
+            for (int j = i * i; j <= nsqrt; j += i)
+                is_prime[j] = false;
+        }
+    }
+
+    int result = 0;
+    vector<char> block(S);
+    for (int k = 0; k * S <= n; k++) {
+        fill(block.begin(), block.end(), true);
+        int start = k * S;
+        for (int p : primes) {
+            int start_idx = (start + p - 1) / p;
+            int j = max(start_idx, p) * p - start;
+            for (; j < S; j += p)
+                block[j] = false;
+        }
+        if (k == 0)
+            block[0] = block[1] = false;
+        for (int i = 0; i < S && start + i <= n; i++) {
+            if (block[i])
+                result++;
+        }
+    }
+    return result;
+}
+
+// Primes in range
+vector<char> segmentedSieve(long long L, long long R) {
+    long long lim = sqrt(R);
+    vector<char> mark(lim + 1, false);
+    vector<long long> primes;
+    for (long long i = 2; i <= lim; ++i) {
+        if (!mark[i]) {
+            primes.emplace_back(i);
+            for (long long j = i * i; j <= lim; j += i)
+                mark[j] = true;
+        }
+    }
+
+    vector<char> isPrime(R - L + 1, true);
+    for (long long i : primes)
+        for (long long j = max(i * i, (L + i - 1) / i * i); j <= R; j += i)
+            isPrime[j - L] = false;
+    if (L == 1)
+        isPrime[0] = false;
+    return isPrime;
+}
+
+int32_t main() {
+    ios_base::sync_with_stdio(0);
+    cin.tie(0);
+
+    int n = 1000000; // Example value, modify as needed
+    cout << "Count of primes up to " << n << ": " << count_primes(n) << '\n';
+
+    long long L = 10, R = 100; // Example range
+    vector<char> primesInRange = segmentedSieve(L, R);
+    cout << "Primes between " << L << " and " << R << ": ";
+    for (long long i = L; i <= R; i++) {
+        if (primesInRange[i - L])
+            cout << i << " ";
+    }
+    cout << '\n';
+
+    return 0;
+}