September Morn Update

Task/Heronian-triangles/Python/heronian-triangles.py

@@ -1,12 +1,10 @@
 from __future__ import division, print_function
-from math import sqrt
-from fractions import gcd
-from itertools import product
+from math import gcd, sqrt
 
 
 def hero(a, b, c):
     s = (a + b + c) / 2
-    a2 = s*(s-a)*(s-b)*(s-c)
+    a2 = s * (s - a) * (s - b) * (s - c)
     return sqrt(a2) if a2 > 0 else 0
 
 
@@ -20,12 +18,24 @@ def gcd3(x, y, z):
 
 
 if __name__ == '__main__':
-    maxside = 200
-    h = [(a, b, c) for a,b,c in product(range(1, maxside + 1), repeat=3)
-         if a <= b <= c and a + b > c and gcd3(a, b, c) == 1 and is_heronian(a, b, c)]
-    h.sort(key = lambda x: (hero(*x), sum(x), x[::-1]))   # By increasing area, perimeter, then sides
-    print('Primitive Heronian triangles with sides up to %i:' % maxside, len(h))
-    print('\nFirst ten when ordered by increasing area, then perimeter,then maximum sides:')
+    MAXSIDE = 200
+
+    N = 1 + MAXSIDE
+    h = [(x, y, z)
+         for x in range(1, N)
+         for y in range(x, N)
+         for z in range(y, N) if (x + y > z) and
+         1 == gcd3(x, y, z) and
+         is_heronian(x, y, z)]
+
+    # By increasing area, perimeter, then sides
+    h.sort(key=lambda x: (hero(*x), sum(x), x[::-1]))
+
+    print(
+        'Primitive Heronian triangles with sides up to %i:' % MAXSIDE, len(h)
+    )
+    print('\nFirst ten when ordered by increasing area, then perimeter,',
+          'then maximum sides:')
     print('\n'.join('  %14r perim: %3i area: %i'
                     % (sides, sum(sides), hero(*sides)) for sides in h[:10]))
     print('\nAll with area 210 subject to the previous ordering:')