# Partition Problem

Emile van Sebille emile at fenx.com
Mon Jul 16 16:30:15 CEST 2001

```Borrowing Tim's klistcombs:

def klistcombs(s, k):
"""Returns list of combinations of S taken K at a time.

S must be a list.
K must be >= 0.
If K > len(S), an empty list is returned.
Else if K is 0, a singleton list containing an empty list
is returned.
The k-combinations are returned in lexicographic order
of their indices.
"""
if k < 0:
raise ValueError, "arg k == %d not >= 0" % k
if len(s) < k:
return []
if k == 0:
return [[]]

indices = range(k)
indices[-1] = indices[-1] - 1
while 1:
limit = len(s) - 1
i = k - 1
while i >= 0 and indices[i] == limit:
i = i - 1
limit = limit - 1
if i < 0:
break
val = indices[i]
for i in xrange( i, k ):
val = val + 1
indices[i] = val
temp = []
for i in indices:
temp.append( s[i] )

def Partition(n,k):
res=[[0]*k]
res[0][0]=(n-k+1)
for x in range(1,k):
res[0][x]=1
current = res[0][:]
for i,j in klistcombs(range(k),2):
while current[i] > current[j]+1:
current[i] -= 1
current[j] += 1
res.append(current[:])
return res

for i in Partition(9,3):
print '\n\n',i

HTH,

--

Emile van Sebille
emile at fenx.com

```