Initial data commit

Task/Mertens-function/Java/mertens-function.java

@@ -0,0 +1,109 @@
+public class MertensFunction {
+
+    public static void main(String[] args) {
+        System.out.printf("First 199 terms of the merten function are as follows:%n    ");
+        for ( int n = 1 ; n < 200 ; n++ ) {
+            System.out.printf("%2d  ", mertenFunction(n));
+            if ( (n+1) % 20 == 0 ) {
+                System.out.printf("%n");
+            }
+        }
+
+        for ( int exponent = 3 ; exponent<= 8 ; exponent++ ) {
+            int zeroCount = 0;
+            int zeroCrossingCount = 0;
+            int positiveCount = 0;
+            int negativeCount = 0;
+            int mSum = 0;
+            int mMin = Integer.MAX_VALUE;
+            int mMinIndex = 0;
+            int mMax = Integer.MIN_VALUE;
+            int mMaxIndex = 0;
+            int nMax = (int) Math.pow(10, exponent);
+            for ( int n = 1 ; n <= nMax ; n++ ) {
+                int m = mertenFunction(n);
+                mSum += m;
+                if ( m < mMin ) {
+                    mMin = m;
+                    mMinIndex = n;
+                }
+                if ( m > mMax ) {
+                    mMax = m;
+                    mMaxIndex = n;
+                }
+                if ( m > 0 ) {
+                    positiveCount++;
+                }
+                if ( m < 0 ) {
+                    negativeCount++;
+                }
+                if ( m == 0 ) {
+                    zeroCount++;
+                }
+                if ( m == 0 && mertenFunction(n - 1) != 0 ) {
+                    zeroCrossingCount++;
+                }
+            }
+            System.out.printf("%nFor M(x) with x from 1 to %,d%n", nMax);
+            System.out.printf("The maximum of M(x) is M(%,d) = %,d.%n", mMaxIndex, mMax);
+            System.out.printf("The minimum of M(x) is M(%,d) = %,d.%n", mMinIndex, mMin);
+            System.out.printf("The sum of M(x) is %,d.%n", mSum);
+            System.out.printf("The count of positive M(x) is %,d, count of negative M(x) is %,d.%n", positiveCount, negativeCount);
+            System.out.printf("M(x) has %,d zeroes in the interval.%n", zeroCount);
+            System.out.printf("M(x) has %,d crossings in the interval.%n", zeroCrossingCount);
+        }
+    }
+
+    private static int MU_MAX = 100_000_000;
+    private static int[] MU = null;
+    private static int[] MERTEN = null;
+
+    //  Compute mobius and merten function via sieve
+    private static int mertenFunction(int n) {
+        if ( MERTEN != null ) {
+            return MERTEN[n];
+        }
+
+        //  Populate array
+        MU = new int[MU_MAX+1];
+        MERTEN = new int[MU_MAX+1];
+        MERTEN[1] = 1;
+        int sqrt = (int) Math.sqrt(MU_MAX);
+        for ( int i = 0 ; i < MU_MAX ; i++ ) {
+            MU[i] = 1;
+        }
+
+        for ( int i = 2 ; i <= sqrt ; i++ ) {
+            if ( MU[i] == 1 ) {
+                //  for each factor found, swap + and -
+                for ( int j = i ; j <= MU_MAX ; j += i ) {
+                    MU[j] *= -i;
+                }
+                //  square factor = 0
+                for ( int j = i*i ; j <= MU_MAX ; j += i*i ) {
+                    MU[j] = 0;
+                }
+            }
+        }
+
+        int sum = 1;
+        for ( int i = 2 ; i <= MU_MAX ; i++ ) {
+            if ( MU[i] == i ) {
+                MU[i] = 1;
+            }
+            else if ( MU[i] == -i ) {
+                MU[i] = -1;
+            }
+            else if ( MU[i] < 0 ) {
+                MU[i] = 1;
+            }
+            else if ( MU[i] > 0 ) {
+                MU[i] = -1;
+            }
+            sum += MU[i];
+            MERTEN[i] = sum;
+        }
+        return MERTEN[n];
+    }
+
+}