Task: Catalan numbers





Java: import java.math.BigInteger;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class CatlanNumbers {

    public static void main(String[] args) {
        Catlan f1 = new Catlan1();
        Catlan f2 = new Catlan2();
        Catlan f3 = new Catlan3();
        System.out.printf("           Formula 1     Formula 2     Formula 3%n");
        for ( int n = 0 ; n <= 15 ; n++ ) {
             System.out.printf("C(%2d) = %,12d  %,12d  %,12d%n", n, f1.catlin(n), f2.catlin(n), f3.catlin(n));
        }
    }
    
    private static interface Catlan {
        public BigInteger catlin(long n);
    }
    
    private static class Catlan1 implements Catlan {

        
        @Override
        public BigInteger catlin(long n) {
            List<Long> numerator = new ArrayList<>();
            for ( long k = n+2 ; k <= 2*n ; k++ ) {
                numerator.add(k);
            }
            
            List<Long> denominator = new ArrayList<>();
            for ( long k = 2 ; k <= n ; k++ ) {
                denominator.add(k);
            }
            
            for ( int i = numerator.size()-1 ; i >= 0  ; i-- ) {
                for ( int j = denominator.size()-1 ; j >= 0  ; j-- ) {
                    if ( denominator.get(j) == 1 ) {
                        continue;
                    }
                    if ( numerator.get(i) % denominator.get(j) == 0 ) {
                        long val = numerator.get(i) / denominator.get(j);
                        numerator.set(i, val);
                        denominator.remove(denominator.get(j));
                        if ( val == 1 ) {
                            break;
                        }
                    }
                }
            }

            BigInteger catlin = BigInteger.ONE;
            for ( int i = 0 ; i < numerator.size() ; i++ ) {
                catlin = catlin.multiply(BigInteger.valueOf(numerator.get(i)));
            }
            for ( int i = 0 ; i < denominator.size() ; i++ ) {
                catlin = catlin.divide(BigInteger.valueOf(denominator.get(i)));
            }
            return catlin;
        }        
    }
    
    private static class Catlan2 implements Catlan {

        private static Map<Long,BigInteger> CACHE = new HashMap<>();
        static {
            CACHE.put(0L, BigInteger.ONE);
        }
        
        
        @Override
        public BigInteger catlin(long n) {
            if ( CACHE.containsKey(n) ) {
                return CACHE.get(n);
            }
            BigInteger catlin = BigInteger.ZERO;
            n--;
            for ( int i = 0 ; i <= n ; i++ ) {
                
                catlin = catlin.add(catlin(i).multiply(catlin(n-i)));
            }
            CACHE.put(n+1, catlin);
            return catlin;
        }
    }
    
    private static class Catlan3 implements Catlan {

        private static Map<Long,BigInteger> CACHE = new HashMap<>();
        static {
            CACHE.put(0L, BigInteger.ONE);
        }
        
        
        @Override
        public BigInteger catlin(long n) {
            if ( CACHE.containsKey(n) ) {
                return CACHE.get(n);
            }
            BigInteger catlin = BigInteger.valueOf(2).multiply(BigInteger.valueOf(2*n-1)).multiply(catlin(n-1)).divide(BigInteger.valueOf(n+1));
            CACHE.put(n, catlin);
            return catlin;
        }
    }

}






Fortran: program main
  
  implicit none

  
  integer                      :: n

  
  double precision, external   :: catalan_numbers         
  
  

  write(*,'(1x,a)')'==============='
  write(*,'(5x,a,6x,a)')'n','c(n)'
  write(*,'(1x,a)')'---------------'

  do n = 0, 14
    write(*,'(1x,i5,i10)') n, int(catalan_numbers(n))
  enddo

  write(*,'(1x,a)')'==============='

  
end program main



double precision recursive function catalan_numbers(n) result(value)
  
  implicit none

  
  integer, intent(in)          :: n

  

  if ( n .eq. 0 ) then
    value = 1
  else 
    value = ( 2.0d0 * dfloat(2 * n - 1) / dfloat( n + 1 ) ) * catalan_numbers(n-1)
  endif

  
end function catalan_numbers