# Subsets II

ArrayBacktrackingBit ## # Solution

This problem follows the easier one.

### # Binary Sorted Subsets

Say there are only five $2$'s in nums, then the following all produce [2 2]:

2 2 2 2 2
---------
1 1 0 0 0 -> [2 2]
1 0 0 0 1 -> [2 2]
0 1 0 1 0 -> [2 2]
0 0 0 1 1 -> [2 2]
...


How do we only take $1$? By observation, there are 3 cases:

1. start w/ $1$'s then followed by $0$'s: 1 1 0...
2. start w/ $1$ but have $0$'s inbetween: 1 0... 1
3. start w/ $0$: 0... 1... or 0... 1... 0...

To only take the 1st case and eliminate the rest 2 cases' duplicates, see the highlighted area below.

def subsetsWithDup(self, nums: List[int]) -> List[List[int]]:
nums.sort()
n = len(nums)
res = []

for mask in range(1 << n):
temp = []
illegal = False
for i in range(n):
not_dup = (i==0) or (i>0 and nums[i-1]==nums[i])
if mask & (1 << i):
# num[i] is duplicate && the former digit of mask is 0
if i>0 and nums[i-1]==nums[i] and mask&(1<<(i-1))==0:
illegal = True
break
else:
temp.append(nums[i])
if not illegal:
res.append(temp)

return res