Fix #9266 : Create knapsack_solver_dp.py

knapsack/knapsack_solver_dp.py

@@ -0,0 +1,49 @@
+"""
+Optimized Dynamic Programming Solution for the 0-1 Knapsack Problem
+
+This implementation finds the maximum value that can be put in a knapsack of capacity `capacity`,
+given a list of item weights and their corresponding values.
+
+Reference: https://en.wikipedia.org/wiki/Knapsack_problem
+
+Usage:
+>>> knapsack(50, [10, 20, 30], [60, 100, 120])
+220
+"""
+
+def knapsack(capacity: int, weights: list[int], values: list[int]) -> int:
+    """
+    Returns the maximum value that can be put in a knapsack of capacity `capacity`,
+    whereby each weight `weights[i]` has a corresponding value `values[i]`.
+
+    :param capacity: The capacity of the knapsack.
+    :param weights: A list of weights for items.
+    :param values: A list of values corresponding to items.
+    :return: The maximum value that can be obtained.
+    >>> knapsack(50, [10, 20, 30], [60, 100, 120])
+    220
+    """
+    n = len(values)
+
+    # Create a DP table with dimensions (n+1) x (capacity+1)
+    dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]
+
+    for i in range(n + 1):
+        for w in range(capacity + 1):
+            if i == 0 or w == 0:
+                dp[i][w] = 0
+            elif weights[i - 1] <= w:
+                # If the current item can fit in the knapsack
+                dp[i][w] = max(values[i - 1] + dp[i - 1][w - weights[i - 1]], dp[i - 1][w])
+            else:
+                # If the current item is too heavy
+                dp[i][w] = dp[i - 1][w]
+
+    return dp[n][capacity]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+