"""Searing Flames: time to reach 5 stacks (2010-06-10)"""

# Copyright (c) 2010 Isoph (US-Scilla)
#
# Permission to use, copy, modify, and/or distribute this software for any
# purpose with or without fee is hereby granted, provided that the above
# copyright notice and this permission notice appear in all copies.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
# WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
# ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
# OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

from math import factorial as fac

# P = sum(i=k..n) ( n! / (i! * (n-i)!) * p^i * (1-p)^(n-i) )
# Formula by Joucifer (US-Illidan)
# http://forums.worldofwarcraft.com/thread.html?sid=1&topicId=25171674646&pageNo=4#61

def P(n, p):
	k = 5
	def each(i):
		return fac(n) / (fac(i) * fac(n-i)) * p**i * (1-p)**(n-i)
	return sum(each(i) for i in xrange(k, n + 1))

if __name__ == '__main__':
	from matplotlib import pyplot as plt
	plt.suptitle(__doc__)
	x = range(5, 31)
	for c, i in zip(('red', 'green', 'blue', 'black'), xrange(1, 5)):
		plt.plot(x, [P(n, i * 0.2) for n in x], c=c, label=("%d/5" % i))
	plt.xlabel('Ticks required')
	plt.xticks(x)
	plt.ylabel('Probability')
	plt.yticks([0.05 * i for i in xrange(21)])
	plt.grid()
	plt.legend(loc='lower right', title='Talent points')
	plt.show()