From 08bfc1a714658ad89a3b379a6b4d8cf7caab10b6 Mon Sep 17 00:00:00 2001
From: Anik Chand <anikchand461@gmail.com>
Date: Sun, 29 Mar 2026 10:13:24 +0530
Subject: [PATCH 1/3] Refactor: clean memoized knapsack using functools.cache

---
 .../knapsack_memoized_clean.py                | 42 +++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 dynamic_programming/knapsack_memoized_clean.py

diff --git a/dynamic_programming/knapsack_memoized_clean.py b/dynamic_programming/knapsack_memoized_clean.py
new file mode 100644
index 000000000000..1c9d3ebb28d7
--- /dev/null
+++ b/dynamic_programming/knapsack_memoized_clean.py
@@ -0,0 +1,42 @@
+from functools import cache
+
+
+def knapsack_memoized(weights: list[int], values: list[int], capacity: int) -> int:
+    """
+    Solve 0/1 knapsack using memoization without global state.
+
+    Args:
+        weights: list of item weights
+        values: list of item values
+        capacity: maximum capacity of knapsack
+
+    Returns:
+        Maximum achievable value
+
+    >>> knapsack_memoized([1, 3, 4], [10, 20, 30], 4)
+    30
+    >>> knapsack_memoized([1, 2, 3], [10, 15, 40], 6)
+    65
+    >>> knapsack_memoized([], [], 5)
+    0
+    """
+
+    if len(weights) != len(values):
+        raise ValueError("weights and values must be of same length")
+
+    n = len(weights)
+
+    @cache
+    def dp(i: int, remaining: int) -> int:
+        if i == n or remaining == 0:
+            return 0
+
+        if weights[i] > remaining:
+            return dp(i + 1, remaining)
+
+        return max(
+            dp(i + 1, remaining),
+            values[i] + dp(i + 1, remaining - weights[i]),
+        )
+
+    return dp(0, capacity)

From 0d77dac9b6e295c2ad4cfbc4d51359bfa51f00d6 Mon Sep 17 00:00:00 2001
From: Anik Chand <anikchand461@gmail.com>
Date: Sun, 29 Mar 2026 10:24:57 +0530
Subject: [PATCH 2/3] Fix: add docstring to dp and improve parameter naming

---
 .../knapsack_memoized_clean.py                | 31 ++++++++++++++-----
 1 file changed, 24 insertions(+), 7 deletions(-)

diff --git a/dynamic_programming/knapsack_memoized_clean.py b/dynamic_programming/knapsack_memoized_clean.py
index 1c9d3ebb28d7..d14b2ae492cd 100644
--- a/dynamic_programming/knapsack_memoized_clean.py
+++ b/dynamic_programming/knapsack_memoized_clean.py
@@ -1,7 +1,9 @@
 from functools import cache
 
 
-def knapsack_memoized(weights: list[int], values: list[int], capacity: int) -> int:
+def knapsack_memoized(
+    weights: list[int], values: list[int], capacity: int
+) -> int:
     """
     Solve 0/1 knapsack using memoization without global state.
 
@@ -19,6 +21,8 @@ def knapsack_memoized(weights: list[int], values: list[int], capacity: int) -> i
     65
     >>> knapsack_memoized([], [], 5)
     0
+    >>> knapsack_memoized([2, 3, 4], [4, 5, 6], 0)
+    0
     """
 
     if len(weights) != len(values):
@@ -27,16 +31,29 @@ def knapsack_memoized(weights: list[int], values: list[int], capacity: int) -> i
     n = len(weights)
 
     @cache
-    def dp(i: int, remaining: int) -> int:
-        if i == n or remaining == 0:
+    def dp(index: int, remaining: int) -> int:
+        """
+        Recursive helper function for knapsack memoization.
+
+        Args:
+            index: current item index
+            remaining: remaining capacity of knapsack
+
+        Returns:
+            Maximum value achievable from current state
+
+        Note:
+            This function is internally tested via knapsack_memoized doctests.
+        """
+        if index == n or remaining == 0:
             return 0
 
-        if weights[i] > remaining:
-            return dp(i + 1, remaining)
+        if weights[index] > remaining:
+            return dp(index + 1, remaining)
 
         return max(
-            dp(i + 1, remaining),
-            values[i] + dp(i + 1, remaining - weights[i]),
+            dp(index + 1, remaining),
+            values[index] + dp(index + 1, remaining - weights[index]),
         )
 
     return dp(0, capacity)

From 51a0d5c67ac698349bf4a15a01b732587925c491 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 29 Mar 2026 04:55:47 +0000
Subject: [PATCH 3/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/knapsack_memoized_clean.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/dynamic_programming/knapsack_memoized_clean.py b/dynamic_programming/knapsack_memoized_clean.py
index d14b2ae492cd..2b8e13d908aa 100644
--- a/dynamic_programming/knapsack_memoized_clean.py
+++ b/dynamic_programming/knapsack_memoized_clean.py
@@ -1,9 +1,7 @@
 from functools import cache
 
 
-def knapsack_memoized(
-    weights: list[int], values: list[int], capacity: int
-) -> int:
+def knapsack_memoized(weights: list[int], values: list[int], capacity: int) -> int:
     """
     Solve 0/1 knapsack using memoization without global state.