Readable code, function docstring and doctests

greedy_methods/fractional_knapsack.py

@@ -1,27 +1,54 @@
 from bisect import bisect
 from itertools import accumulate
 
+# Reference Link: https://en.wikipedia.org/wiki/Continuous_knapsack_problem
 
-def frac_knapsack(vl, wt, w, n):
+
+def frac_knapsack(
+ values: list[int], weights: list[int], capacity: int, max_items: int
+) -> float:
  """
+ This function implements fractional knapsack problem.
+
+ Args:
+ values: List of values of items.
+ weights: List of weights of items.
+ capacity: Capacity of the knapsack.
+ max_items: Number of items.
+
+ Returns:
+ Maximum value of items that can be put into the knapsack.
+
  >>> frac_knapsack([60, 100, 120], [10, 20, 30], 50, 3)
  240.0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 10, 4)
  105.0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 4)
  95.0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6], 8, 4)
- 60.0
+ Traceback (most recent call last):
+ ...
+ ValueError: zip() argument 2 is shorter than argument 1
  >>> frac_knapsack([10, 40, 30], [5, 4, 6, 3], 8, 4)
- 60.0
+ Traceback (most recent call last):
+ ...
+ ValueError: zip() argument 2 is longer than argument 1
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 0, 4)
- 0
+ Traceback (most recent call last):
+ ...
+ ValueError: Capacity and max_items must be greater than 0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 0)
- 95.0
+ Traceback (most recent call last):
+ ...
+ ValueError: Capacity and max_items must be greater than 0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], -8, 4)
- 0
+ Traceback (most recent call last):
+ ...
+ ValueError: Capacity and max_items must be greater than 0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, -4)
- 95.0
+ Traceback (most recent call last):
+ ...
+ ValueError: Capacity and max_items must be greater than 0
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 800, 4)
  130
  >>> frac_knapsack([10, 40, 30, 50], [5, 4, 6, 3], 8, 400)
@@ -30,20 +57,33 @@ def frac_knapsack(vl, wt, w, n):
  Traceback (most recent call last):
  ...
  TypeError: unsupported operand type(s) for /: 'str' and 'int'
+ >>> frac_knapsack([500], [30], 10, 1)
+ 166.66666666666666
  """
 
- r = sorted(zip(vl, wt), key=lambda x: x[0] / x[1], reverse=True)
- vl, wt = [i[0] for i in r], [i[1] for i in r]
- acc = list(accumulate(wt))
- k = bisect(acc, w)
- return (
- 0
- if k == 0
- else sum(vl[:k]) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
- if k != n
- else sum(vl[:k])
+ # Input validation
+ if capacity <= 0 or max_items <= 0:
+ raise ValueError("Capacity and max_items must be greater than 0")
+
+ # sort in descending order of value/weight ratio
+ r = sorted(
+ zip(values, weights, strict=True), key=lambda x: x[0] / x[1], reverse=True
  )
 
+ values, weights = [i[0] for i in r], [i[1] for i in r] # unzip
+ acc = list(accumulate(weights)) # cumulative sum of weights
+
+ # find the index of the weight just greater than capacity
+ k = bisect(acc, capacity)
+
+ if k == 0: # first item is greater than capacity
+ fraction = capacity / weights[0]
+ return fraction * values[0]
+ elif k < max_items: # fractional part of the kth item can be put into the knapsack
+ fraction = (capacity - acc[k - 1]) / weights[k]
+ return sum(values[:k]) + fraction * values[k]
+ return sum(values[:k]) # all items can be put into the knapsack
+
 
 if __name__ == "__main__":
  import doctest