Implementation of the Knapsack Problem Solver #11401

Author: snigdha510

knapsack/dp_knapsack.py

@@ -0,0 +1,30 @@
+def knapsack_dp(capacity: int, weights: list[int], values: list[int]) -> int:
+    """
+    Returns the maximum value that can be put in a knapsack of a given capacity,
+    with each weight having a specific value.
+
+    Uses a dynamic programming approach to solve the 0/1 Knapsack Problem.
+
+    >>> capacity = 50
+    >>> values = [60, 100, 120]
+    >>> weights = [10, 20, 30]
+    >>> knapsack_dp(capacity, weights, values)
+    220
+    """
+    n = len(weights)
+    dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]
+
+    # Build table dp[][] in a bottom-up manner
+    for i in range(1, n + 1):
+        for w in range(1, capacity + 1):
+            if weights[i - 1] <= w:
+                dp[i][w] = max(values[i - 1] + dp[i - 1][w - weights[i - 1]], dp[i - 1][w])
+            else:
+                dp[i][w] = dp[i - 1][w]
+
+    return dp[n][capacity]
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()