I am doing a project that requires getting unique combinations in Python regardless of the subset size.
Lets say I have a list of sizes [1,2,2,3,4,5] and a size bound of 8. I want combinations that have all the elements and no repeat such that the sum of each combination should be less than or equal to 8. Another restriction is that the subtraction of the sum and the bound should be minimum.
For example in this case the answer should be [5,3] [4,2,2] [3,1] this way the total waste out of 8 will be 4 which is (3+1)-8=4.
You could use a recursive function to "brute force" the packing combinations and get the best fit out of those:
def pack(sizes,bound,subset=[]):
if not sizes: # all sizes used
yield [subset] # return current subset
return
if sizes and not subset: # start new subset
i,m = max(enumerate(sizes),key=lambda s:s[1])
subset = [m] # using largest size
sizes = sizes[:i]+sizes[i+1:] # (to avoid repeats)
used = sum(subset)
for i,size in enumerate(sizes): # add to current subset
if subset and size>subset[-1]: # non-increasing order
continue # (to avoid repeats)
if used + size <= bound:
yield from pack(sizes[:i]+sizes[i+1:],bound,subset+[size])
if sizes:
for p in pack(sizes,bound): # add more subsets
yield [subset,*p]
def bestFit(sizes,bound):
packs = pack(sizes,bound)
return min(packs,key = lambda p : bound*len(p)-sum(sizes))
output:
for p in pack([1,2,3,4,5],8):
print(p,8*len(p)-sum(map(sum,p)))
[[5, 1], [4], [3, 2]] 9
[[5, 2, 1], [4, 3]] 1
[[5, 2], [4, 3, 1]] 1
[[5, 2], [4], [3, 1]] 9
[[5, 3], [4, 2, 1]] 1
[[5, 3], [4], [2, 1]] 9
[[5], [4, 1], [3, 2]] 9
[[5], [4, 2], [3, 1]] 9
[[5], [4, 3], [2, 1]] 9
[[5], [4], [3, 2, 1]] 9
[[5], [4], [3], [2, 1]] 17
print(*bestFit([1,2,3,4,5],8))
# [5, 2, 1] [4, 3]
print(*bestFit([1,2,3,4,5,6,7,8,9],18))
# [9, 1] [8, 4, 3, 2] [7, 6, 5]
This will take exponentially longer as your list of sizes gets larger but it may be enough if you only have very small inputs