# Monthly Archives: September 2017

# Prime Sieve in Java

A very concise prime sieve implementation in Java.

/****************************************************************************** * Compilation: javac PrimeSieve.java * Execution: java -Xmx1100m PrimeSieve n * * Computes the number of primes less than or equal to n using * the Sieve of Eratosthenes. * * % java PrimeSieve 25 * The number of primes <= 25 is 9 * * % java PrimeSieve 100 * The number of primes <= 100 is 25 * * % java -Xmx100m PrimeSieve 100000000 * The number of primes <= 100000000 is 5761455 * * % java PrimeSieve -Xmx1100m 1000000000 * The number of primes <= 1000000000 is 50847534 * * * The 110MB and 1100MB is the amount of memory you want to allocate * to the program. If your computer has less, make this number smaller, * but it may prevent you from solving the problem for very large * values of n. * * * n Primes <= n * --------------------------------- * 10 4 * 100 25 * 1,000 168 * 10,000 1,229 * 100,000 9,592 * 1,000,000 78,498 * 10,000,000 664,579 * 100,000,000 5,761,455 * 1,000,000,000 50,847,534 * ******************************************************************************/ public class PrimeSieve { public static void main(String[] args) { int n = Integer.parseInt(args[0]); // initially assume all integers are prime boolean[] isPrime = new boolean[n+1]; for (int i = 2; i <= n; i++) { isPrime[i] = true; } // mark non-primes <= n using Sieve of Eratosthenes for (int factor = 2; factor*factor <= n; factor++) { // if factor is prime, then mark multiples of factor as nonprime // suffices to consider mutiples factor, factor+1, ..., n/factor if (isPrime[factor]) { for (int j = factor; factor*j <= n; j++) { isPrime[factor*j] = false; } } } // count primes int primes = 0; for (int i = 2; i <= n; i++) { if (isPrime[i]) primes++; } System.out.println("The number of primes <= " + n + " is " + primes); } }

# Circle-Angle Formulas

# Merge Sort in Python

def merge(a,b): """ Function to merge two arrays """ c = [] while len(a) != 0 and len(b) != 0: if a[0] < b[0]: c.append(a[0]) a.remove(a[0]) else: c.append(b[0]) b.remove(b[0]) if len(a) == 0: c += b else: c += a return c # Code for merge sort def mergesort(x): """ Function to sort an array using merge sort algorithm """ if len(x) == 0 or len(x) == 1: return x else: middle = round(len(x)/2) a = mergesort(x[:middle]) b = mergesort(x[middle:]) return merge(a,b)