Python编程练习.全排列和全组合

利用Python实现经典算法：全排列和全组合

1.全排列

根据python文档中的itertools.permutations方法进行排列

def permutations(iterable, r=None):
# permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
# permutations(range(3)) --> 012 021 102 120 201 210
pool = tuple(iterable)
n = len(pool)
r = n if r is None else r
if r > n:
return
indices = list(range(n))
cycles = list(range(n, n-r, -1))
yield tuple(pool[i] for i in indices[:r])
while n:
for i in reversed(range(r)):
cycles[i] -= 1
if cycles[i] == 0:
indices[i:] = indices[i+1:] + indices[i:i+1]
cycles[i] = n - i
else:
j = cycles[i]
indices[i], indices[-j] = indices[-j], indices[i]
yield tuple(pool[i] for i in indices[:r])
break
else:
return

2.全组合

(1)根据python文档中的itertools.combinations方法进行排列

def combinations(iterable, r):
# combinations('ABCD', 2) --> AB AC AD BC BD CD
# combinations(range(4), 3) --> 012 013 023 123
pool = tuple(iterable)
n = len(pool)
if r > n:
return
indices = list(range(r))
yield tuple(pool[i] for i in indices)
while True:
for i in reversed(range(r)):
if indices[i] != i + n - r:
break
else:
return
indices[i] += 1
for j in range(i+1, r):
indices[j] = indices[j-1] + 1
yield tuple(pool[i] for i in indices)

(2)根据位运算进行组合

def combinations(str):
n=2**len(str)
for i in range(n):
bits=[i>>offset&1 for offset in range(len(str)-1,-1,-1)]
current=[str[index] for (index,bit) in enumerate(bits) if bit==1]
print(''.join(current));

• 参考：
  【Python: 实现全组合】(https://www.polarxiong.com/archives/Python-实现全组合.html)
  【itertools函数】(https://docs.python.org/3/library/itertools.html?highlight=itertools)