Enhancement of the knapsack algorithm with memorization and generalisation (#9295)

* enhance knapsack problem * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * wei/refactor code * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update test_knapsack.py * Update knapsack.py * Update test_knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update test_knapsack.py --------- Co-authored-by: weijiang <weijiang@weijiangs-MacBook-Pro.local> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: 4 people

knapsack/README.md

@@ -1,4 +1,4 @@
-# A naive recursive implementation of 0-1 Knapsack Problem
+# A recursive implementation of 0-N Knapsack Problem
 
 This overview is taken from:
 

knapsack/knapsack.py

@@ -1,14 +1,23 @@
-"""A naive recursive implementation of 0-1 Knapsack Problem
+"""A recursive implementation of 0-N Knapsack Problem
 https://en.wikipedia.org/wiki/Knapsack_problem
 """
 
 from __future__ import annotations
 
+from functools import lru_cache
 
-def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> int:
+
+def knapsack(
+ capacity: int,
+ weights: list[int],
+ values: list[int],
+ counter: int,
+ allow_repetition=False,
+) -> int:
  """
  Returns the maximum value that can be put in a knapsack of a capacity cap,
- whereby each weight w has a specific value val.
+ whereby each weight w has a specific value val
+ with option to allow repetitive selection of items
 
  >>> cap = 50
  >>> val = [60, 100, 120]
@@ -17,28 +26,40 @@ def knapsack(capacity: int, weights: list[int], values: list[int], counter: int)
  >>> knapsack(cap, w, val, c)
  220
 
- The result is 220 cause the values of 100 and 120 got the weight of 50
+ Given the repetition is NOT allowed,
+ the result is 220 cause the values of 100 and 120 got the weight of 50
  which is the limit of the capacity.
+ >>> knapsack(cap, w, val, c, True)
+ 300
+
+ Given the repetition is allowed,
+ the result is 300 cause the values of 60*5 (pick 5 times)
+ got the weight of 10*5 which is the limit of the capacity.
  """
 
- # Base Case
- if counter == 0 or capacity == 0:
- return 0
-
- # If weight of the nth item is more than Knapsack of capacity,
- # then this item cannot be included in the optimal solution,
- # else return the maximum of two cases:
- # (1) nth item included
- # (2) not included
- if weights[counter - 1] > capacity:
- return knapsack(capacity, weights, values, counter - 1)
- else:
- left_capacity = capacity - weights[counter - 1]
- new_value_included = values[counter - 1] + knapsack(
- left_capacity, weights, values, counter - 1
- )
- without_new_value = knapsack(capacity, weights, values, counter - 1)
- return max(new_value_included, without_new_value)
+ @lru_cache
+ def knapsack_recur(capacity: int, counter: int) -> int:
+ # Base Case
+ if counter == 0 or capacity == 0:
+ return 0
+
+ # If weight of the nth item is more than Knapsack of capacity,
+ # then this item cannot be included in the optimal solution,
+ # else return the maximum of two cases:
+ # (1) nth item included only once (0-1), if allow_repetition is False
+ # nth item included one or more times (0-N), if allow_repetition is True
+ # (2) not included
+ if weights[counter - 1] > capacity:
+ return knapsack_recur(capacity, counter - 1)
+ else:
+ left_capacity = capacity - weights[counter - 1]
+ new_value_included = values[counter - 1] + knapsack_recur(
+ left_capacity, counter - 1 if not allow_repetition else counter
+ )
+ without_new_value = knapsack_recur(capacity, counter - 1)
+ return max(new_value_included, without_new_value)
+
+ return knapsack_recur(capacity, counter)
 
 
 if __name__ == "__main__":

knapsack/tests/test_knapsack.py

@@ -30,7 +30,7 @@ def test_base_case(self):
 
  def test_easy_case(self):
  """
- test for the base case
+ test for the easy case
  """
  cap = 3
  val = [1, 2, 3]
@@ -48,6 +48,16 @@ def test_knapsack(self):
  c = len(val)
  assert k.knapsack(cap, w, val, c) == 220
 
+ def test_knapsack_repetition(self):
+ """
+ test for the knapsack repetition
+ """
+ cap = 50
+ val = [60, 100, 120]
+ w = [10, 20, 30]
+ c = len(val)
+ assert k.knapsack(cap, w, val, c, True) == 300
+
 
 if __name__ == "__main__":
  unittest.main()