'''
Created on Jan 24, 2015
@author: Brett Paufler
Copyright Brett Paufler

Intent is to be a test code snippet utilizing functional paradigms

no reassignment of variables
all variables are functions

Principles of Functional
    Everything is a Function
    No reassignment of Functions/Variables
    
   b = lambda x: x + x 
moves = lambda : 200

virtualJump = lambda (x,y) : random.choice([(x+1,y),(x-1,y),(x,y+1),(x,y-1)])
'''




import math

e = math.e
e213 = 900.0/e
print "Project Euler 213: %.7f" % e213
print "Project Euler 213: %.7f" % (900.0/math.e)

import random

def fleaJump((x,y)):
    a,b = random.choice([(x+1,y),(x-1,y),(x,y+1),(x,y-1)])
    if a<0 or b<0 or a>29 or b>29:
        return fleaJump((x,y))
    else:
        return (a,b)

#virtualJump = lambda (x,y) : random.choice([(x+1,y),(x-1,y),(x,y+1),(x,y-1)])
#fleaJump = lambda (x,y) : virtualJump(x,y)

def jumpAll(fleaList):
    fleasNext = []
    for flea in fleaList:
        fleasNext.append(fleaJump(flea))
    return fleasNext

fleaStart = [(a,b) for a in range(30) for b in range(30)]

turn = [fleaStart]

moves = 200
for m in range(moves):
    turn.append(jumpAll(turn[-1]))

emptySquaresPerTurn = [900 - len(set(t)) for t in turn]
average = sum(emptySquaresPerTurn[100:]) / float(moves-100)

print average