feat: sieve algorithm was updated

LuchoBazz · web-flow · commit cbc502a205e7 · 2022-07-13T15:19:16.000-05:00
diff --git a/math/math_sieve.cpp b/math/math_sieve.cpp
@@ -1,56 +1,16 @@
-class Sieve {
-    int maximum;
-    vector<int> primes;
-    vector<int> smallest_factor;
-    vector<bool> isprime;
-public:
-    
-    Sieve() : maximum(-1) {}
-
-    Sieve(int mx) : maximum(mx) {
-        assert(0 <= mx);
-        isprime.resize(maximum+1, true);
-        smallest_factor.resize(maximum+1, 0);
-        
-        smallest_factor[0] = smallest_factor[1] = 1;
-        isprime[0] = isprime[1] = false;
-        
-        for(int prime = 2; prime <= maximum; ++prime) {
-            if(isprime[prime]) {
-                primes.push_back(prime);
-                smallest_factor[prime] = prime;
-                for(int64_t j = 1LL*prime*prime; j <= maximum; j += prime) {
-                    if(isprime[j]) {
-                        isprime[j] = false;
-                        smallest_factor[j] = prime;
-                    }
-                }
-            }
-        }
-    }
-
-    int prime_kth(int k) {
-        // returns the k-th prime (1-indexed)
-        assert(1 <= k && k <= (int) primes.size());
-        return primes[k-1];
-    }
-    
-    int size_primes() {
-        // number of primes from 0 to maximum (inclusive)
-        return (int) primes.size();
-    }
-
-    int smallest(int number) { // smallest prime factor of a number
-        assert(1 <= number && number <= maximum);
-        return smallest_factor[number];
-    }
-
-    bool is_prime(int number) {
-        assert(0 <= number && number <= maximum);
-        return isprime[number];
-    }
-
-    bool operator[](int number) {
-        return is_prime(number);
-    }
-};
+// using int64 = long long;
+
+const int M = 1e6 + 2;
+bool marked[M+1];
+vector<int> primes;
+
+// Time: O(M*log(log(M)))
+void sieve() {
+    marked[0] = marked[1] = true;
+    for (int i = 2; i <= M; i++) {
+        if (marked[i]) continue;
+        primes.push_back(i);
+        for (int64 j = 1LL * i * i; j <= M; j += i)
+            marked[j] = true;
+    }
+}
diff --git a/math/math_sieve_full.cpp b/math/math_sieve_full.cpp
@@ -0,0 +1,56 @@
+class Sieve {
+    int maximum;
+    vector<int> primes;
+    vector<int> smallest_factor;
+    vector<bool> isprime;
+public:
+    
+    Sieve() : maximum(-1) {}
+
+    Sieve(int mx) : maximum(mx) {
+        assert(0 <= mx);
+        isprime.resize(maximum+1, true);
+        smallest_factor.resize(maximum+1, 0);
+        
+        smallest_factor[0] = smallest_factor[1] = 1;
+        isprime[0] = isprime[1] = false;
+        
+        for(int prime = 2; prime <= maximum; ++prime) {
+            if(isprime[prime]) {
+                primes.push_back(prime);
+                smallest_factor[prime] = prime;
+                for(int64_t j = 1LL*prime*prime; j <= maximum; j += prime) {
+                    if(isprime[j]) {
+                        isprime[j] = false;
+                        smallest_factor[j] = prime;
+                    }
+                }
+            }
+        }
+    }
+
+    int prime_kth(int k) {
+        // returns the k-th prime (1-indexed)
+        assert(1 <= k && k <= (int) primes.size());
+        return primes[k-1];
+    }
+    
+    int size_primes() {
+        // number of primes from 0 to maximum (inclusive)
+        return (int) primes.size();
+    }
+
+    int smallest(int number) { // smallest prime factor of a number
+        assert(1 <= number && number <= maximum);
+        return smallest_factor[number];
+    }
+
+    bool is_prime(int number) {
+        assert(0 <= number && number <= maximum);
+        return isprime[number];
+    }
+
+    bool operator[](int number) {
+        return is_prime(number);
+    }
+};
