# Combinations from itertools behaving weird

## Question:

I need to identify pairs of subsets of the same size such that they are disjoint and that if we order the sets A={a_1<a_2<…<a_m} and B{b_1<b_2<…<b_m} then for every i=1,…,m a_i<b_i.

Here’s my code:

``````n=7
cont=0
for m in range(2,n//2+1):
combs=combinations(list(range(n)),m)
combs=[set(comb) for comb in combs]
print(combs)
pairs=[(comb1,comb2) for comb1 in combs for comb2 in combs if comb1.intersection(comb2)==set()]
pairs=[pair for pair in pairs if npmin(list(pair[0]))<npmin(list(pair[1]))]
flag=True
for pair in pairs:
l1=list(pair[0])
l2=list(pair[1])
l1.sort()
l2.sort()
flag=True
for n in range(m):
flag=flag and l1[n]<l2[n]
if not flag:
cont+=1
cont
``````

The expected output for this case, n=7, would be 70.

But, here’s the thing, for the second iteration, m=3, the list combs is empty, so that for m=3 cont stays the same value, and the code then outputs a 35. I can’t understand why. Any help is welcomed!

It’s unclear what you’re trying to do.

However, I made a few changes, that might help.

First, you can use `SortedSet()` so that you don’t have to `sort()` every time.

For `m == 3`, it prints

### combs

[(0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 1, 5), (0, 1, 6), (0, 2, 3), (0,
2, 4), (0, 2, 5), (0, 2, 6), (0, 3, 4), (0, 3, 5), (0, 3, 6), (0, 4,
5), (0, 4, 6), (0, 5, 6), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),
(1, 3, 4), (1, 3, 5), (1, 3, 6), (1, 4, 5), (1, 4, 6), (1, 5, 6), (2,
3, 4), (2, 3, 5), (2, 3, 6), (2, 4, 5), (2, 4, 6), (2, 5, 6), (3, 4,
5), (3, 4, 6), (3, 5, 6), (4, 5, 6)]

Right?

• I guess you don’t want the same var names for `n`, `combs` and `pairs`.
``````
from itertools import combinations
import numpy as np
from sortedcontainers import SortedSet

def f(n):
cont = 0
for m in range(2, n // 2 + 1):
if m > n:
continue

combs = combinations(list(range(n)), m)
# if m == 3:
#     print(list(combs))
#     break
scombs = [set(comb) for comb in combs]
pairs = [(comb1, comb2) for comb1 in scombs for comb2 in scombs if comb1.intersection(comb2) == SortedSet()]
spairs = [pair for pair in pairs if np.min(list(pair[0])) < np.min(list(pair[1]))]
for l1, l2 in spairs:
flag = True
l1, l2 = list(l1), list(l2)
for i in range(m):
flag = flag and l1[i] < l2[i]
if not flag:
cont += 1
return cont

print(f(7))

``````

70

### Note

• Make sure you’re passing the correct `n` (inclusive) to `combinations`, if that’s what you want:
``````combs = combinations(list(range(n + 1)), m)
``````
• You also forgot to add `if m > n: continue`.
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