How do I get a list of every possible combination of product prices to reach a target cost?

Question

Suppose I have a list of three products (A, B C). Each Product has a price. Given a total cost, I want to find all the possible product combinations to equal exactly that co

Answer 1

The itertools module offers combinatoric generators to help with problems such as this:

>>> from itertools import *
>>> prices = dict(a=10, b=15, c=8, d=2, e=5)
>>> total_cost = 20
>>> for r in range(1, 30):
        for t in combinations_with_replacement(prices, r):
                cost = sum(prices[p] for p in t)
                if cost == total_cost:
                        print t

Answer 2

def possibilities(available_products, target_price):
    if target_price == 0 or not available_products:
        return []
    this_price = available_products[0]
    remaining_products = available_products[1:]
    results = []
    for qty in range(1 + target_price / this_price):
        remaining_price = target_price - qty*this_price
        if remaining_price == 0:
            results.append([qty] + [0] * len(remaining_products))
        else:
            for option in possibilities(remaining_products, remaining_price):
                results.append([qty] + option)
    return results

That gives you:

pprint.pprint(possibilities([1, 2, 5], 10))
[[0, 0, 2],
 [0, 5, 0],
 [1, 2, 1],
 [2, 4, 0],
 [3, 1, 1],
 [4, 3, 0],
 [5, 0, 1],
 [6, 2, 0],
 [8, 1, 0],
 [10, 0, 0]]