Python - Combination of Numbers Summing to Greater than or Equal to a Value

Question

I was recently posed the following interview question to be answered in Python - given a list of quantity-value pairs, find the optimal combination(s) of sets of values whose sum is as close to, and at least as large as, some provided value.

For example, given: [(1, $5), (3, $10), (2, $15)], and a desired value of $36, the answer would be [(2,$15), (1,$10)] or [(1,$15), (2,$10), (1,$5)]. The reason is that $40 is the least sum greater than or equal to $36 that can be achieved, and these are the two ways to achieve that sum.

I got stumped. Does anyone have a solution?

Answer 1

The numbers are so small you can just brute force it:

In []:
notes = [(1, 5), (3, 10), (2, 15)]
wallet = [n for a, b in notes for n in [b]*a]
combs = {sum(x): x for i in range(1, len(wallet)) for x in it.combinations(wallet, i)}

target = 36
for i in sorted(combs):
    if i >= target:
        break
i, combs[i]

Out[]:
(40, (5, 10, 10, 15))

You can extend this for all combinations, just replace the combs dictionary comprehension with:

combs = {}
for i in range(1, len(wallet)):
    for x in it.combinations(wallet, i):
        combs.setdefault(sum(x), set()).add(x)

...
i, combs[i]

Out[]:
(40, {(5, 10, 10, 15), (10, 15, 15)})