Rod Cutting in C#

using System;
// Rod Cutting in C#
//
// PURPOSE
// Rod cutting chooses cuts that maximize the sale value of a rod. It considers every first
// piece and reuses the optimal solution for the remaining length.
//
// METHOD
// Set the value of length zero to zero. For each length, try each possible first cut and
// combine its price with the already computed remainder value.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space.
//
// CONTRACT
// prices[i] is the nonnegative price for length i+1 and contains n entries. Returns maximum
// revenue for length n. Revenue must fit.
// 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: 10.
// 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 rod_cutting(ReadOnlySpan<int> prices, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            int[] dp = new int[alg_size((n + 1))];
            int length = 1;
            int cut = 0;
            while ((length <= n)) {
                cut = 1;
                while ((cut <= length)) {
                    dp[length] = Math.Max(dp[length], (prices[(cut - 1)] + dp[(length - cut)]));
                    cut = (cut + 1);
                }
                length = (length + 1);
            }
            return dp[n];
        }
    }

    static void Main() {
        int[] prices = new int[] {1, 5, 8, 9};
        int n = 4;
        int result = rod_cutting(prices, n);
        Console.WriteLine(result);
    }
}