Python中的快速组合生成器

Question

作为python中一个大型项目的一部分，我需要一个快速生成器函数来生成所有可能的小于n的非负整数集，这样每个集合最多有s个元素，并且集合中最大和最小数字之间的差小于w。在

到目前为止，我实现的最快的实现是使用itertools：

import itertools

def subsample(n, s, w):
    nn = range(w)
    for p in range(s):
        o = list(itertools.combinations(nn, p+1))
        for t in o:
            yield t
        for _ in range(0, n-w):
            pt = o
            o = [tuple([op + 1 for op in list(u)]) for u in pt]
            for t in list((set(o) ^ set(pt)) & set(o)):
                yield t

例如：

^{pr2}$

但我相信，必须有更有效的方法来做到这一点。有什么能让这更快的吗？在

Answer 1

下面是一些基于Knuth算法的生成器。在

• subsets4生成1..n具有k或更少元素的所有子集
• subsets5将subsets4生成的子集限制为最大差w
• subsets生成1..n长度正好k的所有子集
• subsets2将subsets生成的子集限制为最大差w

运行megatest()函数来测试subsets5生成器是否存在多个n、k和w的多个值。在

# all subsets of k or less elements of 1..n
def subsets4(n,k):
  a = [ 0 ] * k
  i = 0
  while i >= 0:
    a[i] += 1
    yield a[0:i+1]
    r = a[i]+1
    i += 1
    while i < k and r <= n:
      a[i] = r
      yield a[0:i+1]
      i += 1
      r += 1
    i -= 1
    if a[i] >= n:
      i -= 1

# all subsets of k or less elements of 1..n with max difference <= w
def subsets5(n,k,w):
  a = [ 0 ] * k
  i = 0
  while i >= 0:
    a[i] += 1
    yield a[0:i+1]
    r = a[i]+1
    i += 1
    while i < k and r <= n and r-a[0] <= w:
      a[i] = r
      yield a[0:i+1]
      i += 1
      r += 1
    i -= 1
    if a[i] >= n or a[i]+1-a[0] > w:
      i -= 1

# all subsets of 1..n having exactly k elements
def subsets(n,k):
  a = range(1,k+1)
  while a[0] <= n+1-k:
    yield a
    # find i
    i = k-1
    while i >= 0 and a[i]+k-i >= n+1: i -= 1
    r = a[i]
    a[i] += 1
    j = 2
    i += 1
    while i < k:
      a[i] = r + j
      i += 1
      j += 1

# all subsets of 1..n having exactly k elements and whose max
# difference is w
def subsets2(n,k,w):
  if k > w: return
  a = range(1,k+1)
  while a[0] <= n+1-k:
    yield a
    i = k-1
    while i >= 0 and (a[i]+k-i >= n+1 or a[i]+k-i-a[0] > w) : i -= 1
    r = a[i]
    a[i] += 1
    j = 2
    i += 1
    while i < k:
      a[i] = r + j
      i += 1
      j += 1

def test(n,k,w):
  s1 = [ s for s in subsets4(n,k) if s[-1] - s[0] <= w ]
  s2 = [ s for s in subsets5(n,k,w) ]
  if s1 == s2:
    print "OK", n,k,w
    return 0
  else:
    print "NOT OK", n, k, w
    return 1 

# for s in subsets2(10,3,4): print s
# for s in subsets(10,3): print s
def megatest():
  failed = 0
  for n in xrange(10,20):
    for k in xrange(1,n+1):
      for w in xrange(k,n+1):
        failed += test(n,k,w)
  print "failed:", failed