Fractional Knapsack

def fractionalKnapsack(values, weights, capacity):
    n = len(values)
    used = [False] * n
    total = 0
    room = capacity
    while room > 0:
        best = -1
        for i in range(n):
            # i is denser than best: values[i] / weights[i] > values[best] / weights[best], cross-multiplied
            if not used[i] and (best == -1 or values[i] * weights[best] > values[best] * weights[i]):
                best = i
        if best == -1:
            break  # every item is already in the bag
        used[best] = True
        if weights[best] <= room:
            total += values[best]
            room -= weights[best]
        else:
            total += values[best] * room // weights[best]  # the part that fits, rounded down
            room = 0
    return total

from functools import cmp_to_key


def fractionalKnapsack(values, weights, capacity):
    # a goes before b when values[a] / weights[a] > values[b] / weights[b],
    # tested as values[a] * weights[b] > values[b] * weights[a] to stay in whole numbers.
    def denser_first(a, b):
        return values[b] * weights[a] - values[a] * weights[b]

    order = sorted(range(len(values)), key=cmp_to_key(denser_first))
    total = 0
    room = capacity
    for i in order:
        if weights[i] <= room:
            total += values[i]  # the whole item fits
            room -= weights[i]
        else:
            total += values[i] * room // weights[i]  # the part that fits, rounded down
            break
    return total