Combinatoric solution using Pascal's Triangle to Problem 15

Author: daniel-s-ingram

Project Euler/Problem 15/sol1.py

@@ -0,0 +1,20 @@
+from __future__ import print_function
+from math import factorial, ceil
+
+def lattice_paths(n):
+	n = 2*n #middle entry of odd rows starting at row 3 is the solution for n = 1, 2, 3,...
+	k = n/2
+
+	return factorial(n)/(factorial(k)*factorial(n-k))
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		print(lattice_paths(20))
+	else:
+		try:
+			n = int(sys.argv[1])
+			print(lattice_paths(n))
+		except ValueError:
+			print('Invalid entry - please enter a number.')