Here's a possible solution. I'm sure others will comment on how to
fix up its inefficiencies (like the potentially slow string
concatenations...).
def comb(n, k):
if n == k == 0:
yield ''
else:
if n > 0:
for x in comb(n-1, k):
yield ' ' + x
if k > 0:
for x in comb(n, k-1):
yield '|' + x
def boxings(n, k):
if k == 0:
if n == 0:
yield []
else:
for s in comb(n, k-1):
yield map(len, (''.join(s)).split('|'))
for b in boxings(4, 3):
print b
Output:
[4, 0, 0]
[3, 1, 0]
[3, 0, 1]
[2, 2, 0]
[2, 1, 1]
[2, 0, 2]
[1, 3, 0]
[1, 2, 1]
[1, 1, 2]
[1, 0, 3]
[0, 4, 0]
[0, 3, 1]
[0, 2, 2]
[0, 1, 3]
[0, 0, 4]
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