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

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+from math import sqrt
+from fractions import gcd
+from itertools import product
+
+
+def hero(a, b, c):
+    s = (a + b + c) / 2
+    a2 = s*(s-a)*(s-b)*(s-c)
+    return sqrt(a2) if a2 > 0 else 0
+
+
+def is_heronian(a, b, c):
+    a = hero(a, b, c)
+    return a > 0 and a.is_integer()
+
+
+def gcd3(x, y, z):
+    return gcd(gcd(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:')
+    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:')
+    print('\n'.join('  %14r perim: %3i area: %i'
+                    % (sides, sum(sides), hero(*sides)) for sides in h
+                    if hero(*sides) == 210))