user40680 - 5 months ago 5
Python Question

# Permutations with Order

I am trying to write a Python function that performs a function similar to

`itertools.permutation`
.

``````import itertools
for s in itertools.permutations("TCGA****")
print s
``````

The ideal output from such a function would be

``````('*','*','*','*','T', 'C','G','A')
('*','*','*','T','*', 'C','G','A')
('*','*','*','T','C', '*','G','A')
('*','*','*','T','C', 'G','*','A')
('*','*','*','T','C', 'G','A','*')
('*','*','T','C','G', 'A','*','*')
('*','*','T','C','G', '*','*','A')
('*','*','T','C','*', '*','G','A')
...
('T', 'C','G','A','*','*','*','*')
``````

The only difference between
`itertools.permutation`
and this function is that the order is maintained i.e. 'T' always precedes 'C' which precedes 'G' which precedes 'A'.

The following is an example that violates this rule

``````('*','*','T','*','G','C','A','*','*')
``````

The order of 'C' and 'G' has changed.

How can I produce the permutations for which the order
`'TGCA'`
is maintained among the asterisks?

One idea would be to produce all the possible indices for your `'*'` values with `itertools.combinations` on your list index range, and then construct each possible permutation from those indices, filling with your `'TCGA'` values accordingly for the indices not found in each combination.

Since you are assured to use all of `TCGA` in each iteration, `itertools.cycle` is one way to continually get the appropriate value for the next position.

``````from itertools import combinations, cycle

char_cyc = cycle('TCGA')
combos = combinations(range(8), 4)

perms = [['*' if i in combo else next(char_cyc) for i in range(8)]
for combo in combos]

print(perms)
``````

Outputs:

``````[['*', '*', '*', '*', 'T', 'C', 'G', 'A'], ['*', '*', '*', 'T', '*', 'C', 'G', 'A'], ['*', '*', '*', 'T', 'C', '*', 'G', 'A'], ['*', '*', '*', 'T', 'C', 'G', '*', 'A'], ['*', '*', '*', 'T', 'C', 'G', 'A', '*'], ['*', '*', 'T', '*', '*', 'C', 'G', 'A'], ['*', '*', 'T', '*', 'C', '*', 'G', 'A'], ['*', '*', 'T', '*', 'C', 'G', '*', 'A'], ['*', '*', 'T', '*', 'C', 'G', 'A', '*'], ['*', '*', 'T', 'C', '*', '*', 'G', 'A'], ['*', '*', 'T', 'C', '*', 'G', '*', 'A'], ['*', '*', 'T', 'C', '*', 'G', 'A', '*'], ['*', '*', 'T', 'C', 'G', '*', '*', 'A'], ['*', '*', 'T', 'C', 'G', '*', 'A', '*'], ['*', '*', 'T', 'C', 'G', 'A', '*', '*'], ['*', 'T', '*', '*', '*', 'C', 'G', 'A'], ['*', 'T', '*', '*', 'C', '*', 'G', 'A'], ['*', 'T', '*', '*', 'C', 'G', '*', 'A'], ['*', 'T', '*', '*', 'C', 'G', 'A', '*'], ['*', 'T', '*', 'C', '*', '*', 'G', 'A'], ['*', 'T', '*', 'C', '*', 'G', '*', 'A'], ['*', 'T', '*', 'C', '*', 'G', 'A', '*'], ['*', 'T', '*', 'C', 'G', '*', '*', 'A'], ['*', 'T', '*', 'C', 'G', '*', 'A', '*'], ['*', 'T', '*', 'C', 'G', 'A', '*', '*'], ['*', 'T', 'C', '*', '*', '*', 'G', 'A'], ['*', 'T', 'C', '*', '*', 'G', '*', 'A'], ['*', 'T', 'C', '*', '*', 'G', 'A', '*'], ['*', 'T', 'C', '*', 'G', '*', '*', 'A'], ['*', 'T', 'C', '*', 'G', '*', 'A', '*'], ['*', 'T', 'C', '*', 'G', 'A', '*', '*'], ['*', 'T', 'C', 'G', '*', '*', '*', 'A'], ['*', 'T', 'C', 'G', '*', '*', 'A', '*'], ['*', 'T', 'C', 'G', '*', 'A', '*', '*'], ['*', 'T', 'C', 'G', 'A', '*', '*', '*'], ['T', '*', '*', '*', '*', 'C', 'G', 'A'], ['T', '*', '*', '*', 'C', '*', 'G', 'A'], ['T', '*', '*', '*', 'C', 'G', '*', 'A'], ['T', '*', '*', '*', 'C', 'G', 'A', '*'], ['T', '*', '*', 'C', '*', '*', 'G', 'A'], ['T', '*', '*', 'C', '*', 'G', '*', 'A'], ['T', '*', '*', 'C', '*', 'G', 'A', '*'], ['T', '*', '*', 'C', 'G', '*', '*', 'A'], ['T', '*', '*', 'C', 'G', '*', 'A', '*'], ['T', '*', '*', 'C', 'G', 'A', '*', '*'], ['T', '*', 'C', '*', '*', '*', 'G', 'A'], ['T', '*', 'C', '*', '*', 'G', '*', 'A'], ['T', '*', 'C', '*', '*', 'G', 'A', '*'], ['T', '*', 'C', '*', 'G', '*', '*', 'A'], ['T', '*', 'C', '*', 'G', '*', 'A', '*'], ['T', '*', 'C', '*', 'G', 'A', '*', '*'], ['T', '*', 'C', 'G', '*', '*', '*', 'A'], ['T', '*', 'C', 'G', '*', '*', 'A', '*'], ['T', '*', 'C', 'G', '*', 'A', '*', '*'], ['T', '*', 'C', 'G', 'A', '*', '*', '*'], ['T', 'C', '*', '*', '*', '*', 'G', 'A'], ['T', 'C', '*', '*', '*', 'G', '*', 'A'], ['T', 'C', '*', '*', '*', 'G', 'A', '*'], ['T', 'C', '*', '*', 'G', '*', '*', 'A'], ['T', 'C', '*', '*', 'G', '*', 'A', '*'], ['T', 'C', '*', '*', 'G', 'A', '*', '*'], ['T', 'C', '*', 'G', '*', '*', '*', 'A'], ['T', 'C', '*', 'G', '*', '*', 'A', '*'], ['T', 'C', '*', 'G', '*', 'A', '*', '*'], ['T', 'C', '*', 'G', 'A', '*', '*', '*'], ['T', 'C', 'G', '*', '*', '*', '*', 'A'], ['T', 'C', 'G', '*', '*', '*', 'A', '*'], ['T', 'C', 'G', '*', '*', 'A', '*', '*'], ['T', 'C', 'G', '*', 'A', '*', '*', '*'], ['T', 'C', 'G', 'A', '*', '*', '*', '*']]
``````

A good indication that is output is correct is the fact that the length of `perms` is 70, which is equal to 8C4 (or "8 choose 4"), which is effectively what your problem concerns.

Source (Stackoverflow)