# Fractional Knapsack

alelom

2,454 views

## INPUTS

## Values

values = "10,3,4,7" # You can change these.

## Weights

weights = "2,5,1,3" # You can change these.

## Knapsack total capacity

capacity = 10

## ALGORITHM

def fractional_knapsack(values, weights, capacity): # index = [0, 1, 2, ..., n - 1] for n items index = list(range(len(values)))

```
# value/weight ratio
ratio = [v / w for v, w in zip(values, weights)]
# index sorted by descending value/weight ratio
index.sort(key=lambda i: ratio[i], reverse=True)
print(index)
max_value = 0
fractions = [0] * len(values)
for i in index:
if weights[i] <= capacity:
fractions[i] = 1
max_value += values[i]
capacity -= weights[i]
else:
fractions[i] = capacity / weights[i]
max_value += values[i] * capacity / weights[i]
break
return max_value, fractions
```

## Process inputs

values = [int(v) for v in values.split(',')] weights = [int(w) for w in weights.split(',')]

## FUNCTION CALL

max_value, fractions = fractional_knapsack(values, weights, capacity)

## Output

print('Total value that can be carried:', max_value) print('Fractions by which to multiply the items:', fractions)

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