# Solution of;
# Project Euler Problem 503: Compromise or persist
# https://projecteuler.net/problem=503
# 
# Alice is playing a game with n cards numbered 1 to n. A game consists of 
# iterations of the following steps. (1) Alice picks one of the cards at 
# random. (2) Alice cannot see the number on it. Instead, Bob, one of her 
# friends, sees the number and tells Alice how many previously-seen numbers 
# are bigger than the number which he is seeing. (3) Alice can end or continue 
# the game. If she decides to end, the number becomes her score. If she 
# decides to continue, the card is removed from the game and she returns to 
# (1). If there is no card left, she is forced to end the game. Let F(n) be 
# the Alice's expected score if she takes the optimized strategy to minimize 
# her score. For example, F(3) = 5/3. At the first iteration, she should 
# continue the game. At the second iteration, she should end the game if Bob 
# says that one previously-seen number is bigger than the number which he is 
# seeing, otherwise she should continue the game. We can also verify that F(4) 
# = 15/8 and F(10) ≈ 2. 5579365079. Find F(106). Give your answer rounded to 
# 10 decimal places behind the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 503
    timed.caller(dummy, n, i, prob_id)
