gistfile1.py

'''
  Project Euler problem 477
  url: https://projecteuler.net/problem=477
'''
import sys

def sequence_gen(n):
    ret = 0
    i   = 0
    while i < n:
        yield ret
        ret = ((ret**2) + 45) % 1000000007
        i += 1

def get_n(n):
    return [i for i in sequence_gen(n)].pop()

def _pop_index(seq):
    if seq[0] >= seq[-1]:
        return 0
    else:
        return -1

def _score_move(seq, move = 0):
    score = 0
    # move is either 0 or -1
    sequence = list(seq)
    score += sequence.pop(move)
    while len(sequence) > 0:
        # opponent move
        score -= sequence.pop(_pop_index(sequence))
        if len(sequence) > 0:
        # self move
            score += sequence.pop(_pop_index(sequence))
    return score

def score(seq):
    # score a is the score for the 0th element
    score_a = 0
    # score b is the score for the -1th element
    score_b = 0
    # start by trying the first element
    score_a = _score_move(seq, 0)
    # then try the last element
    score_b = _score_move(seq, -1)
    #debugging
    print "score_a: %i \nscore_b: %i" % (score_a, score_b)
    if score_a >= score_b:
        return 0
    else:
        return -1

def solve(n):
    p1_score = 0
    p2_score = 0
    seq = [num for num in sequence_gen(n)]
    while len(seq) > 0:
        # player 1 moves
        p1_score += seq.pop(score(seq))
        if len(seq) > 0:
            # player 2 moves
            p2_score += seq.pop(score(seq))
    return p1_score, p2_score

if __name__ == '__main__':
    if len(sys.argv) > 1:
        r = solve(int(sys.argv[1]))
        print "player 1 score: %i" % r[0]
        print "player 2 score: %i" % r[1]

it gives 25344091514 as F(100) some logic issue I see in choosing the elements.
We need to compare either to choose first or last if they are largest in all four 1,2, last and second last element. (value at index 0,1 or n, n-1 )
if 0 or n is not largest, then
if 1 is largest choose n
if n-1 is largest choose 1.
So that Player 2 had to choose other and we can get largest in next move.