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Pythagorean triples/Java/Brute force primitives (view source)

Revision as of 20:45, 20 December 2011

75 bytes removed ,  12 years ago
m
Somewhere in there I got rid of the need for 12 as a BigInteger, reformat
(This is what I was really looking for when I made that last optimization)
m (Somewhere in there I got rid of the need for 12 as a BigInteger, reformat)
 
(3 intermediate revisions by the same user not shown)
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{{works with|Java|1.5+}}
This version brute forces primitive triple candidates and then scales them to find the rest (under the perimeter limit of course). Since it only finds the primitives mathematically it can optimize its candidates based on some of the properties [[wp:Pythagorean_triple#Elementary_properties_of_primitive_Pythagorean_triples|here]] -- namely that a and b have opposite evenness, only one of a and b is divisible by 3, only one of a and b is divisible by 4, c is always odd, and that a<sup>2</sup> + b<sup>2</sup> must be a perfect square (which [[wp:Square_number#Properties|don't ever end in 2, 3, 7, or 8]]). NotablyAfter using those rules to eliminate candidates for a,b pairs, it doesn'tchecks usethat a GCDand functionb toare checkcoprime. forSince primitivesmany (<code>BigInteger.gcd()</code>a,b usespair thecandidates binaryhave GCDalready algorithmbeen eliminated, [[wp:Computational_complexity_of_mathematical_operations#Number_theory|whichthis ischeck O(n<sup>2</sup>)]])actually speeds things up a little bit by letting the program skip some c loops. For a perimeter limit of 1000, it is about 5 times faster than [[Pythagorean triples#Java|the other brute force version]]. For a perimeter limit of 10000, it is about 1517 times faster. It also does not markmarks the primitives.
 
It defines a <code>Triple</code> class which is comparable so it can be placed in a <code>SetTreeSet</code> for easy sorting and to remove duplicates (e.g.the thisGCD algorithmcheck findsshould [15,remove 20duplicates, 25] as a primitive candidate afterbut it's hadnice alreadyto been added by scaling [3, 4,make 5]sure). It also can scale itself by an integer factor.
 
Note: this implementation also keeps all triples in memory. Be mindful of large perimeter limits.
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import java.util.Set;
import java.util.TreeSet;
 
import static java.math.BigInteger.*;
 
public class PythTrip2PythTrip{
publicprivate static final BigInteger TWO = BigInteger.valueOf(2),
B3 = BigInteger.valueOf(3), B3B4 = BigInteger.valueOf(34),
B7 = BigInteger.valueOf(7), B4B31 = BigInteger.valueOf(431),
B7B127 = BigInteger.valueOf(7127), B191 //used= for checking primitive propertiesBigInteger.valueOf(191);
//change this to whatever perimeter limit you want;the RAM's the limit▼
B12 = BigInteger.valueOf(12),▼
private static BigInteger B31LIMIT = BigInteger.valueOf(31100),;
 
B127 = BigInteger.valueOf(127),▼
public static class Triple implements Comparable<Triple>{▼
B191 = BigInteger.valueOf(191);
BigInteger a, b, c, peri;
▲ //change this to whatever perimeter limit you want;the RAM's the limit
boolean prim;▼
private static BigInteger LIMIT = BigInteger.valueOf(100);
 
▼
public Triple(BigInteger a, BigInteger b, BigInteger c, boolean prim){
▲ public static class Triple implements Comparable<Triple>{
BigInteger this.a, b,= c, peria;
}this.b = b;▼
publicthis.c Triple(BigInteger a, BigInteger b, BigInteger= c) {;
this.aperi = a.add(b).add(c);
this.bprim = bprim;
this.c = c;}
 
peri = a.add(b).add(c);▼
public Triple scale(long }k){
▲ return new B127 = Triple(a.multiply(BigInteger.valueOf(127k)), b
▲
▲ B12 = .multiply(BigInteger.valueOf(12k)), c.multiply(BigInteger
public Triple scale(long k){▼
return new Triple(a.multiply(BigInteger.valueOf(k)), prim && k == 1);
▲ }
b.multiply(BigInteger.valueOf(k)),
 
c.multiply(BigInteger.valueOf(k)));
}@Override
▲ public Tripleboolean scaleequals(longObject kobj){
@Overrideif(obj.getClass() != this.getClass())
public boolean equals(Object obj) {return false;
Triple trip if(obj.getClass() != this.getClass()Triple) return falseobj;
return a.equals(trip.a) && Triple b.equals(trip.b) =&& c.equals(Tripletrip.c)obj;
}▼
return a.equals(trip.a) && b.equals(trip.b) && c.equals(trip.c);
 
▲ }
@Override▼
public int compareTo(Triple @Overrideo){
public int compareToif(!a.equals(Triple o.a)) {
//sort byreturn a, then b, then c.compareTo(o.a);
if(!ab.equals(o.ab)) return a.compareTo(o.a);
if(!b.equals(o.b)) return b.compareTo(o.b);
if(!c.equals(o.c)) return c.compareTo(o.c);
return 0c.compareTo(o.c);
}return 0;
}
 
▲ @Override
public String toString(){
return a + ", " + b + ", " + c + (prim ? " primitive" : "");
}
}
 
▲
private static Set<Triple> trips = new TreeSet<Triple>();
 
public static void addAllScales(Triple trip){
long k = 2;
Triple tripCopy = new Triple(trip.a, trip.b, trip.cscale(k++);
while(tripCopy.peri.compareTo(LIMIT) <= 0){
trips.add(tripCopy);
tripCopy = trip.scale(k++);
}
}
 
public static void main(String[] args){
long primCount = 0;
long start = System.currentTimeMillis();
 
BigInteger peri2 = LIMIT.divide(TWO), peri3 = LIMIT.divide(B3);
peri3 = LIMIT.divide(B3);▼
 
for(BigInteger a = B3; a.compareTo(peri3) < 0; a = a.add(ONE)){
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//b is the opposite evenness of a so increment by 2
for(BigInteger b = a.add(ONE); b.compareTo(peri2) < 0; b = b
b.compareTo(peri2) < 0; b = b.add(TWO)){
//skip if both or neither of a and b are divisible by each of 3 and 4
if(amod3 == b.mod(B3).equals(ZERO) ||
|| amod4 == b.mod(B4).equals(ZERO)) continue;
//if a^2 + b^2 is not a perfect square then don't even test for c'scontinue;
//if a^2+b^2 isn't a perfect square, don't even test for c's
BigInteger aabb = aa.add(b.multiply(b));
if((aabb.and(B7).intValue() != 1) &&
&& (aabb.and(B31).intValue() != 4) &&
&& (aabb.and(B127).intValue() != 16) &&
&& (aabb.and(B191).intValue() != 0)) continue;
▲ peri = a.add(b).add(c)continue;
if(!a.gcd(b).equals(ONE))
▲ peri3 = LIMIT.divide(B3) continue;
BigInteger ab = a.add(b);
 
for(BigInteger// c =is always odd for primitives so if b.add(b.testBit(0) ?is TWO:ONE);odd start at b+2
// otherwise c.compareTo(peri2) < 0; c = c.add(TWO)){b+1
for(BigInteger c = b.add(b.testBit(0) //if? a+b+cZERO >: periLimitONE); c
if(ab.add(c) .compareTo(LIMITperi2) >< 0; c = c.add(TWO)){
 
break;▼
}// if a+b+c > periLimit
if(ab.add(c).compareTo(LIMIT) > 0) break;
 
int compare = aabb.compareTo(c.multiply(c));
// if a^2 + b^2 != c^2
if(compare < 0){
break;
}else if (compare == 0){
Triple prim = new Triple(a, b, c, true);
if(trips.add(prim)){ //if it's new
primCount++; //count it
addAllScales(prim); //add its scales
}
}
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}
}
for(Triple trip : trips){
System.out.println(trip);
}
System.out.println("Runtime: " + (System.currentTimeMillis() - start));
System.out.println("Up to a perimeter of " + LIMIT + ", there are "
+ trips.size() + " triples, of which " + primCount + " are primitive.");
▲ + " are breakprimitive.");
}
}</lang>
Output:
<pre>3, 4, 5 primitive
5, 12, 13 primitive
6, 8, 10
7, 24, 25 primitive
8, 15, 17 primitive
9, 12, 15
9, 40, 41 primitive
10, 24, 26
12, 16, 20
12, 35, 37 primitive
15, 20, 25
15, 36, 39
16, 30, 34
18, 24, 30
20, 21, 29 primitive
21, 28, 35
24, 32, 40
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