Data commit

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

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+from __future__ import division, print_function
+from math import gcd, sqrt
+
+
+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
+
+    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:')
+    print('\n'.join('  %14r perim: %3i area: %i'
+                    % (sides, sum(sides), hero(*sides)) for sides in h
+                    if hero(*sides) == 210))