Data update

Task/Multi-base-primes/Java/multi-base-primes.java

@@ -0,0 +1,111 @@
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.Collections;
+import java.util.List;
+
+public final class MultibasePrimes {
+
+	public static void main(String[] aArgs) {
+		final int maxBase = 36;
+		final int maxLength = 5;	
+		fillPrimes(maxBase, maxLength);		
+		multibasePrimes(maxBase, maxLength);		
+	}		
+	
+	private static void multibasePrimes(int aMaxBase, int aMaxLength) {
+		for ( int length = 1; length <= aMaxLength; length++ ) {	
+	        int maxBasesCount = 0;
+	        List<Tuple> maxStrings = new ArrayList<Tuple>();
+	        List<Integer> digits = new ArrayList<Integer>(Collections.nCopies(length, 0));
+	        digits.set(0, 1);
+	        List<Integer> bases = new ArrayList<Integer>();
+	
+	        do {
+	            final int maxDigit = digits.stream().max(Integer::compare).get();
+	            final int minBase = Math.max(2, maxDigit + 1);
+	            if ( maxBasesCount > aMaxBase - minBase + 1 ) {
+	                continue;
+	            }
+	            bases.clear();
+	
+	            for ( int base = minBase; base <= aMaxBase; base++ ) {
+	                if ( aMaxBase - base + 1 + bases.size() < maxBasesCount ) {
+	                    break;
+	                }
+	                int number = 0;
+	                for ( int digit : digits ) {
+	                    number = number * base + digit;
+	                }
+	                if ( primes[number] ) {
+	                    bases.add(base);
+	                }
+	            }
+	
+	            if ( bases.size() > maxBasesCount ) {
+	                maxBasesCount = bases.size();
+	                maxStrings.clear();
+	            }
+	            if ( bases.size() == maxBasesCount ) {
+	                maxStrings.add( new Tuple( new ArrayList<Integer>(digits), new ArrayList<Integer>(bases) ) );
+	            }
+	
+	        } while ( increment(digits, aMaxBase) );
+	
+	        System.out.println(length + "-character strings which are prime in the most bases: " + maxBasesCount);
+	        for ( Tuple tuple : maxStrings ) {
+	            System.out.println(numberBase(tuple.first) + " -> " + tuple.second);
+	        }
+	        System.out.println();
+	    }
+	}
+	
+	private static boolean increment(List<Integer> aDigits, int aMaxBase) {
+	    for ( int i = aDigits.size() - 1; i >= 0; i-- ) {
+	        if ( aDigits.get(i) + 1 != aMaxBase ) {
+	            aDigits.set(i, aDigits.get(i) + 1);	
+	            return true;
+	        }
+	        aDigits.set(i, 0);
+	    }
+	    return false;
+	}
+	
+	private static String numberBase(List<Integer> aList) {
+	    final String digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+	    StringBuilder result = new StringBuilder();
+	    for ( int number : aList ) {
+	        result.append(digits.charAt(number));
+	    }
+	    return result.toString();
+	}
+	
+	private static void fillPrimes(int aMaxBase, int aMaxLength) {
+		final int limit = (int) Math.pow(aMaxBase, aMaxLength);
+		primes = new boolean[limit + 1];
+		Arrays.fill(primes, true);
+		primes[0] = false;
+		primes[1] = false;
+		for ( int i = 2; i < Math.sqrt(limit); i++ ) {
+			if ( primes[i] ) {
+				int j = i * i;
+				while ( j <= limit ) {
+					primes[j] = false;
+					j += i;
+				}
+			}
+		}
+	}
+	
+	private static class Tuple {
+		
+		public Tuple(List<Integer> aFirst, List<Integer> aSecond) {
+			first = aFirst; second = aSecond;
+		}
+		
+		private List<Integer> first, second;		
+		
+	}
+	
+	private static boolean[] primes;
+	
+}