We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies.
  1. Prepare
  2. Algorithms
  3. Recursion
  4. Bowling Pins
  5. Discussions

Bowling Pins

  • urupica
     + 3 comments

    Excellent analysis!

    Here is a great article that explains all the necessary theory: nim.pdf

    I solved it using the game theory approach and found a much shorter solution (Python 2):

    # precompute the Sprague-Grundy (SG) function for all 0 <= n <= 300
g = [0, 1, 2]
for n in xrange(3, 301):
    s = set()
    # hit one or two pins
    for l in (1, 2):
        # the group of n pins can be split into two 
        # grops of i and n - l - i pins
        for i in xrange((n - l)/2 + 1):
            s.add(g[i]^g[n - l - i])
    # compute mex (minimum excluded value)
    m = 0
    while m in s:
        m += 1
    g.append(m)

for t in xrange(int(raw_input().strip())):
    raw_input()
    ret = 0
    # split the pins into groups and xor the SG values
    for p in raw_input().strip().split('X'):
        ret ^= g[len(p)]
    print 'WIN' if ret else 'LOSE'