Fractional Knapsack

def fractional_knapsack(value, weight, capacity):
    """Return maximum value of items and their fractional amounts.
 
    (max_value, fractions) is returned where max_value is the maximum value of
    items with total weight not more than capacity.
    fractions is a list where fractions[i] is the fraction that should be taken
    of item i, where 0 <= i < total number of items.
 
    value[i] is the value of item i and weight[i] is the weight of item i
    for 0 <= i < n where n is the number of items.
 
    capacity is the maximum weight.
    """
    # index = [0, 1, 2, ..., n - 1] for n items
    index = list(range(len(value)))
    # contains ratios of values to weight
    ratio = [v/w for v, w in zip(value, weight)]
    # index is sorted according to value-to-weight ratio in decreasing order
    index.sort(key=lambda i: ratio[i], reverse=True)
 
    max_value = 0
    fractions = [0]*len(value)
    for i in index:
        if weight[i] <= capacity:
            fractions[i] = 1
            max_value += value[i]
            capacity -= weight[i]
        else:
            fractions[i] = capacity/weight[i]
            max_value += value[i]*capacity/weight[i]
            break
 
    return max_value, fractions
 
 
n = int(input('Enter number of items: '))
value = input('Enter the values of the {} item(s) in order: '
              .format(n)).split()
value = [int(v) for v in value]
weight = input('Enter the positive weights of the {} item(s) in order: '
               .format(n)).split()
weight = [int(w) for w in weight]
capacity = int(input('Enter maximum weight: '))
 
max_value, fractions = fractional_knapsack(value, weight, capacity)
print('The maximum value of items that can be carried:', max_value)
print('The fractions in which the items should be taken:', fractions)
Program Explanation
1. The user is prompted to enter the number of items n.
2. The user is then asked to enter n values and n weights.
3. The function fractional_knapsack is called to get the maxmimum value and the list of fractions.
4. The result is then displayed.