Data commit

Task/Legendre-prime-counting-function/Java/legendre-prime-counting-function.java

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+import java.util.*;
+
+public class LegendrePrimeCounter {
+    public static void main(String[] args) {
+        LegendrePrimeCounter counter = new LegendrePrimeCounter(1000000000);
+        for (int i = 0, n = 1; i < 10; ++i, n *= 10)
+            System.out.printf("10^%d\t%d\n", i, counter.primeCount((n)));
+    }
+
+    private List<Integer> primes;
+
+    public LegendrePrimeCounter(int limit) {
+        primes = generatePrimes((int)Math.sqrt((double)limit));
+    }
+
+    public int primeCount(int n) {
+        if (n < 2)
+            return 0;
+        int a = primeCount((int)Math.sqrt((double)n));
+        return phi(n, a) + a - 1;
+    }
+
+    private int phi(int x, int a) {
+        if (a == 0)
+            return x;
+        if (a == 1)
+            return x - (x >> 1);
+        int pa = primes.get(a - 1);
+        if (x <= pa)
+            return 1;
+        return phi(x, a - 1) - phi(x / pa, a - 1);
+    }
+
+    private static List<Integer> generatePrimes(int limit) {
+        boolean[] sieve = new boolean[limit >> 1];
+        Arrays.fill(sieve, true);
+        for (int p = 3, s = 9; s < limit; p += 2) {
+            if (sieve[p >> 1]) {
+                for (int q = s; q < limit; q += p << 1)
+                    sieve[q >> 1] = false;
+            }
+            s += (p + 1) << 2;
+        }
+        List<Integer> primes = new ArrayList<>();
+        if (limit > 2)
+            primes.add(2);
+        for (int i = 1; i < sieve.length; ++i) {
+            if (sieve[i])
+                primes.add((i << 1) + 1);
+        }
+        return primes;
+    }
+}