Making good single-elimination tourney brackets based on seeds. Optimally orders the bracket so that worse seeds get knocked out first by people as close as possible to their skill level.

tourney.py

def tourney_in_order(k):
  """
  Tells you the bracket for a tourney with n=2^k competitors 1-n, where 1
  is the best. The bracket is such that competitors lose in the order of
  their skill to the person with a level of skill as close to theirs as
  possible.

  >>> bracket = tourney_in_order(4)
  >>> print bracket
  [16, 8, 15, 4, 14, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9, 1]
  """
  n = 2**k
  bracket = [None]*n
  i = n
  for r in range(k+1):
    m1 = 2**(r+1)
    m2 = 0 if r==0 else (2**r -1)
    j = m2
    while j < n:
      bracket[j] = i
      j += m1
      i -= 1
  return bracket

def tourney_fair(k):
  """
  Tells you the bracket for a tourney with n=2^k competitors 1-n, where 1
  is the best. The bracket is optimally fair subject to making competitors
  lose in the correct round.
  >>> bracket = tourney_fair(4)
  >>> print bracket
  [16, 8, 12, 4, 14, 6, 10, 2, 15, 7, 11, 3, 13, 5, 9, 1]
  """
  n = 2**k
  bracket = [n]
  s = n/2
  for _ in range(k):
    bracket += [ i - s for i in bracket ]
    s /= 2
  return bracket

from math import log, ceil
def next_2exp(n):
  """
  Returns the exponent of the next largest power of 2. I.e. returns
  ceil(log2(n)). Helpful for switching from n=2^k to k.
  >>> next_2exp(19)
  5
  """
  if n <= 0:
    return -float("inf")
  return int(ceil(log(n, 2)))