0-1 Knapsack in C#

using System;
// 0-1 Knapsack in C#
//
// PURPOSE
// Knapsack chooses items with maximum total value under a weight limit, using each item at
// most once. The one-dimensional table stores the best value for each capacity.
//
// METHOD
// Process items one at a time and capacities downward. Compare skipping the item with adding
// its value to the previous best at the remaining capacity. Descending capacities prevent
// reusing the current item.
//
// COMPLEXITY
// O(n * capacity) time and O(capacity) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Weights are positive, values nonnegative, capacity >= 0. Both arrays have n entries.
// Returns best value, not the chosen item set.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 9.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int knapsack(ReadOnlySpan<int> weights, ReadOnlySpan<int> values, int capacity) {
        checked {
            int n = weights.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((weights.Length == n));
            alg_require((values.Length == n));
            alg_require(((capacity >= 0) && (capacity <= 1000000)));
            for (int alg_i = 0; alg_i < weights.Length; alg_i++) {
                int alg_value = weights[alg_i];
                alg_require((alg_value > 0));
            }
            for (int alg_i = 0; alg_i < values.Length; alg_i++) {
                int alg_value = values[alg_i];
                alg_require((alg_value >= 0));
            }
            int[] dp = new int[alg_size((capacity + 1))];
            int i = 0;
            int c = 0;
            while ((i < n)) {
                c = capacity;
                while ((c >= weights[i])) {
                    dp[c] = Math.Max(dp[c], (dp[(c - weights[i])] + values[i]));
                    c = (c - 1);
                }
                i = (i + 1);
            }
            return dp[capacity];
        }
    }

    static void Main() {
        int[] weights = new int[] {2, 3, 4};
        int[] values = new int[] {4, 5, 7};
        int capacity = 5;
        int result = knapsack(weights, values, capacity);
        Console.WriteLine(result);
    }
}