# Revision history [back]

Here is a possible recursive (rather lazy) implementation without using specialized iter tools.

def mySplitIntoPieces(S, L):
"""S is a list of "elements",
L is a list of positive integers with sum(L) = len(S),
we want to return the list of all tuples
[ S0, S1, S2, ... ]
where S0, S1, S2, ... are a partition of S and
len(S0) = L[0],
len(S1) = L[1],
len(S2) = L[2],
and so on.
"""

if len(S) != sum(L):
return

if len(L) == 0:
return [ S ]    # the partition of S in one piece

return [ [ S0, ] + furtherPieces
for S0 in Combinations( S, L[0] )
for furtherPieces in mySplitIntoPieces( list(set(S).difference(S0)), L[1:] ) ]


Let us test the functionality:

sage: for pieces in mySplitIntoPieces( [0..4], [2,1,2] ):
....:     print(pieces)
[[0, 1], [2], [3, 4]]
[[0, 1], [3], [2, 4]]
[[0, 1], [4], [2, 3]]
[[0, 2], [1], [3, 4]]
[[0, 2], [3], [1, 4]]
[[0, 2], [4], [1, 3]]
[[0, 3], [1], [2, 4]]
[[0, 3], [2], [1, 4]]
[[0, 3], [4], [1, 2]]
[[0, 4], [1], [2, 3]]
[[0, 4], [2], [1, 3]]
[[0, 4], [3], [1, 2]]
[[1, 2], [0], [3, 4]]
[[1, 2], [3], [0, 4]]
[[1, 2], [4], [0, 3]]
[[1, 3], [0], [2, 4]]
[[1, 3], [2], [0, 4]]
[[1, 3], [4], [0, 2]]
[[1, 4], [0], [2, 3]]
[[1, 4], [2], [0, 3]]
[[1, 4], [3], [0, 2]]
[[2, 3], [0], [1, 4]]
[[2, 3], [1], [0, 4]]
[[2, 3], [4], [0, 1]]
[[2, 4], [0], [1, 3]]
[[2, 4], [1], [0, 3]]
[[2, 4], [3], [0, 1]]
[[3, 4], [0], [1, 2]]
[[3, 4], [1], [0, 2]]
[[3, 4], [2], [0, 1]]
sage: