Subset Sum Decision in C#

using System;
// Subset Sum Decision in C#
//
// PURPOSE
// Subset sum asks whether some selection of items totals an exact target. A reachability
// table records which sums can be formed.
//
// METHOD
// Mark zero reachable. For each item, scan sums downward and mark a sum reachable if it
// already was or if the sum minus the item was reachable before this item.
//
// COMPLEXITY
// O(n * target) time and O(target) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Items and target are nonnegative integers. Each input position can be used once. Returns 1
// if reachable, otherwise 0.
// 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: 1.
// 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 subset_sum(ReadOnlySpan<int> a, int target) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require(((target >= 0) && (target <= 1000000)));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require((alg_value >= 0));
            }
            int[] dp = new int[alg_size((target + 1))];
            dp[0] = 1;
            int i = 0;
            int s = 0;
            while ((i < n)) {
                s = target;
                while ((s >= a[i])) {
                    if ((dp[(s - a[i])] != 0)) {
                        dp[s] = 1;
                    }
                    s = (s - 1);
                }
                i = (i + 1);
            }
            return dp[target];
        }
    }

    static void Main() {
        int[] a = new int[] {3, 4, 5};
        int target = 9;
        int result = subset_sum(a, target);
        Console.WriteLine(result);
    }
}