Task: Pythagorean triples





Java: import java.math.BigInteger;
import static java.math.BigInteger.ONE;

public class PythTrip{

    public static void main(String[] args){
        long tripCount = 0, primCount = 0;

        
        BigInteger periLimit = BigInteger.valueOf(100),
                peri2 = periLimit.divide(BigInteger.valueOf(2)),
                peri3 = periLimit.divide(BigInteger.valueOf(3));

        for(BigInteger a = ONE; a.compareTo(peri3) < 0; a = a.add(ONE)){
            BigInteger aa = a.multiply(a);
            
            for(BigInteger b = a.add(ONE);
                    b.compareTo(peri2) < 0; b = b.add(ONE)){
                BigInteger bb = b.multiply(b);
                BigInteger ab = a.add(b);
                BigInteger aabb = aa.add(bb);
                
                for(BigInteger c = b.add(ONE);
                        c.compareTo(peri2) < 0; c = c.add(ONE)){

                    int compare = aabb.compareTo(c.multiply(c));
                    
                    if(ab.add(c).compareTo(periLimit) > 0){
                        break;
                    }
                    
                    if(compare < 0){
                        break;
                    }else if (compare == 0){
                        tripCount++;
                        System.out.print(a + ", " + b + ", " + c);

                        
                        if(a.gcd(b).equals(ONE)){
                            System.out.print(" primitive");
                            primCount++;
                        }
                        System.out.println();
                    }
                }
            }
        }
        System.out.println("Up to a perimeter of " + periLimit + ", there are "
                + tripCount + " triples, of which " + primCount + " are primitive.");
    }
}



Python: from fractions import gcd


def pt1(maxperimeter=100):
    
    trips = []
    for a in range(1, maxperimeter):
        aa = a*a
        for b in range(a, maxperimeter-a+1):
            bb = b*b
            for c in range(b, maxperimeter-b-a+1):
                cc = c*c
                if a+b+c > maxperimeter or cc > aa + bb: break
                if aa + bb == cc:
                    trips.append((a,b,c, gcd(a, b) == 1))
    return trips

def pytrip(trip=(3,4,5),perim=100, prim=1):
    a0, b0, c0 = a, b, c = sorted(trip)
    t, firstprim = set(), prim>0
    while a + b + c <= perim:
        t.add((a, b, c, firstprim>0))
        a, b, c, firstprim = a+a0, b+b0, c+c0, False
    
    t2 = set()
    for a, b, c, firstprim in t:
        a2, a5, b2, b5, c2, c3, c7 = a*2, a*5, b*2, b*5, c*2, c*3, c*7
        if  a5 - b5 + c7 <= perim:
            t2 |= pytrip(( a - b2 + c2,  a2 - b + c2,  a2 - b2 + c3), perim, firstprim)
        if  a5 + b5 + c7 <= perim:
            t2 |= pytrip(( a + b2 + c2,  a2 + b + c2,  a2 + b2 + c3), perim, firstprim)
        if -a5 + b5 + c7 <= perim:
            t2 |= pytrip((-a + b2 + c2, -a2 + b + c2, -a2 + b2 + c3), perim, firstprim)
    return t | t2

def pt2(maxperimeter=100):
    
    trips = pytrip((3,4,5), maxperimeter, 1)
    return trips

def printit(maxperimeter=100, pt=pt1):
    trips = pt(maxperimeter)
    print("  Up to a perimeter of %i there are %i triples, of which %i are primitive"
          % (maxperimeter,
             len(trips),
             len([prim for a,b,c,prim in trips if prim])))
  
for algo, mn, mx in ((pt1, 250, 2500), (pt2, 500, 20000)):
    print(algo.__doc__)
    for maxperimeter in range(mn, mx+1, mn):
        printit(maxperimeter, algo)