From c93841eb9468cf6433e057a230d60063cfcd1dd8 Mon Sep 17 00:00:00 2001
From: nickzerjeski <nick@zerjeski.de>
Date: Sat, 11 Apr 2026 16:18:01 +0200
Subject: [PATCH 1/3] Add space optimized 0/1 knapsack implementation

---
 dynamic_programming/knapsack.py | 34 +++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)

diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py
index 28c5b19dbe36..ecdb38e7989c 100644
--- a/dynamic_programming/knapsack.py
+++ b/dynamic_programming/knapsack.py
@@ -39,6 +39,40 @@ def knapsack(w, wt, val, n):
     return dp[n][w_], dp
 
 
+def knapsack_space_optimized(
+    capacity: int, weights: list[int], values: list[int], num_items: int
+) -> int:
+    """
+    Solve the 0/1 knapsack problem with O(capacity) extra space.
+
+    It uses a 1D dynamic programming array and iterates capacities in reverse
+    for each item to avoid reusing the same item more than once.
+
+    >>> knapsack_space_optimized(50, [10, 20, 30], [60, 100, 120], 3)
+    220
+    >>> knapsack_space_optimized(0, [10, 20, 30], [60, 100, 120], 3)
+    0
+    >>> knapsack_space_optimized(6, [4, 3, 2, 3], [3, 2, 4, 4], 4)
+    8
+    """
+    if num_items < 0:
+        raise ValueError("The number of items cannot be negative.")
+    if capacity < 0:
+        raise ValueError("The knapsack capacity cannot be negative.")
+    if num_items > len(weights) or num_items > len(values):
+        raise ValueError("The number of items exceeds the provided input lengths.")
+
+    dp = [0] * (capacity + 1)
+    for item_index in range(num_items):
+        item_weight = weights[item_index]
+        item_value = values[item_index]
+        for current_capacity in range(capacity, item_weight - 1, -1):
+            dp[current_capacity] = max(
+                dp[current_capacity], item_value + dp[current_capacity - item_weight]
+            )
+    return dp[capacity]
+
+
 def knapsack_with_example_solution(w: int, wt: list, val: list):
     """
     Solves the integer weights knapsack problem returns one of

From 07539cb4d9f849628ab46d21c801f9714c4987cb Mon Sep 17 00:00:00 2001
From: nickzerjeski <nick@zerjeski.de>
Date: Sat, 11 Apr 2026 16:50:31 +0200
Subject: [PATCH 2/3] Harden knapsack_space_optimized input validation

---
 dynamic_programming/knapsack.py | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py
index ecdb38e7989c..a6500543deec 100644
--- a/dynamic_programming/knapsack.py
+++ b/dynamic_programming/knapsack.py
@@ -54,6 +54,26 @@ def knapsack_space_optimized(
     0
     >>> knapsack_space_optimized(6, [4, 3, 2, 3], [3, 2, 4, 4], 4)
     8
+    >>> knapsack_space_optimized(-1, [1], [1], 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: The knapsack capacity cannot be negative.
+    >>> knapsack_space_optimized(1, [1], [1], -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: The number of items cannot be negative.
+    >>> knapsack_space_optimized(1, [1], [1], 2)
+    Traceback (most recent call last):
+        ...
+    ValueError: The number of items exceeds the provided input lengths.
+    >>> knapsack_space_optimized(1, [-1], [1], 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Weight at index 0 cannot be negative.
+    >>> knapsack_space_optimized(1, [1], [1.5], 1)
+    Traceback (most recent call last):
+        ...
+    TypeError: Value at index 0 must be an integer.
     """
     if num_items < 0:
         raise ValueError("The number of items cannot be negative.")
@@ -61,6 +81,15 @@ def knapsack_space_optimized(
         raise ValueError("The knapsack capacity cannot be negative.")
     if num_items > len(weights) or num_items > len(values):
         raise ValueError("The number of items exceeds the provided input lengths.")
+    for item_index in range(num_items):
+        item_weight = weights[item_index]
+        item_value = values[item_index]
+        if not isinstance(item_weight, int):
+            raise TypeError(f"Weight at index {item_index} must be an integer.")
+        if item_weight < 0:
+            raise ValueError(f"Weight at index {item_index} cannot be negative.")
+        if not isinstance(item_value, int):
+            raise TypeError(f"Value at index {item_index} must be an integer.")
 
     dp = [0] * (capacity + 1)
     for item_index in range(num_items):

From 3fb7cf30b4a7bc899828eb7eca8e746fb2d0dfb3 Mon Sep 17 00:00:00 2001
From: nickzerjeski <nick@zerjeski.de>
Date: Sat, 11 Apr 2026 16:56:26 +0200
Subject: [PATCH 3/3] Fix ruff EM102 in knapsack_space_optimized

---
 dynamic_programming/knapsack.py | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py
index a6500543deec..9d5155cdd7e8 100644
--- a/dynamic_programming/knapsack.py
+++ b/dynamic_programming/knapsack.py
@@ -85,11 +85,14 @@ def knapsack_space_optimized(
         item_weight = weights[item_index]
         item_value = values[item_index]
         if not isinstance(item_weight, int):
-            raise TypeError(f"Weight at index {item_index} must be an integer.")
+            msg = f"Weight at index {item_index} must be an integer."
+            raise TypeError(msg)
         if item_weight < 0:
-            raise ValueError(f"Weight at index {item_index} cannot be negative.")
+            msg = f"Weight at index {item_index} cannot be negative."
+            raise ValueError(msg)
         if not isinstance(item_value, int):
-            raise TypeError(f"Value at index {item_index} must be an integer.")
+            msg = f"Value at index {item_index} must be an integer."
+            raise TypeError(msg)
 
     dp = [0] * (capacity + 1)
     for item_index in range(num_items):