tasks a-s

Task/Pythagorean-triples/CoffeeScript/pythagorean-triples.coffeescript

@@ -0,0 +1,33 @@
+gcd = (x, y) ->
+  return x if y == 0
+  gcd(y, x % y)
+
+# m,n generate primitive Pythag triples
+#
+# preconditions:
+#   m, n are integers of different parity
+#   m > n
+#   gcd(m,n) == 1 (coprime)
+#
+# m, n generate: [m*m - n*n, 2*m*n, m*m + n*n]
+# perimeter is 2*m*m + 2*m*n = 2 * m * (m+n)
+count_triples = (max_perim) ->
+  num_primitives = 0
+  num_triples = 0
+  m = 2
+  upper_limit = Math.sqrt max_perim / 2
+  while m <= upper_limit
+    n = m % 2 + 1
+    p = 2*m*m + 2*m*n
+    delta = 4*m
+    while n < m and p <= max_perim
+      if gcd(m, n) == 1
+        num_primitives += 1
+        num_triples += Math.floor max_perim / p
+      n += 2
+      p += delta
+    m += 1
+  console.log num_primitives, num_triples
+
+max_perim = Math.pow 10, 9 # takes under a minute
+count_triples(max_perim)