Solving the Josephus problem via recursion

josephus.py

#CS352  Homework 2, Summer '12
#Victoria Wu
#Josephus Problem
#-----------------
#N people are in a circle, with first person (1) holding a hot potato.
#After M passes of the potato, the person holding the potato is out, and the
#game continues with the next person in line picking up the potato.
#Continue until one person remains. Who will be the victor, given (N>0, M>=0)?


#Number the people from 0 to N-1

#kill(people-1, passes) is the position of the survivor in the next
#iteration of the circle.

#kill(people-1, passes) + passes is the position of the NEXT person who is out.

#The last person who would have been out is the winner. This function returns the
#last person to be "out", thus the minus one to find the winner.

def kill(people, passes):
    #If there is one person left, no need to continue.
    if people ==1:
        return 0
    return ((kill(people-1,passes)+passes) % people )

people = int(raw_input("Please enter how many people (N) :"))

passes = int(raw_input("Please enter number of passes (M) :"))

winner = kill(people, passes)-1
if winner < 0:
    winner = people

print "Player %d wins!" %(winner)