tasks a-s

Task/Pythagorean-triples/Python/pythagorean-triples-1.py

@@ -0,0 +1,56 @@
+from fractions import gcd
+
+
+def pt1(maxperimeter=100):
+    '''
+# Naive method
+    '''
+    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):
+    '''
+# Parent/child relationship method:
+# http://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples#XI.
+    '''
+    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)

Task/Pythagorean-triples/Python/pythagorean-triples-2.py

@@ -0,0 +1,14 @@
+from sys import setrecursionlimit
+setrecursionlimit(2000) # 2000 ought to be big enough for everybody
+
+def triples(lim, a = 3, b = 4, c = 5):
+	l = a + b + c
+	if l > lim: return (0, 0)
+	return reduce(lambda x, y: (x[0] + y[0], x[1] + y[1]), [
+		(1, lim / l),
+		triples(lim,  a - 2*b + 2*c,  2*a - b + 2*c,  2*a - 2*b + 3*c),
+		triples(lim,  a + 2*b + 2*c,  2*a + b + 2*c,  2*a + 2*b + 3*c),
+		triples(lim, -a + 2*b + 2*c, -2*a + b + 2*c, -2*a + 2*b + 3*c) ])
+
+for peri in [10 ** e for e in range(1, 8)]:
+	print peri, triples(peri)

Task/Pythagorean-triples/Python/pythagorean-triples-3.py

@@ -0,0 +1,7 @@
+10 (0, 0)
+100 (7, 17)
+1000 (70, 325)
+10000 (703, 4858)
+100000 (7026, 64741)
+1000000 (70229, 808950)
+10000000 (702309, 9706567)