Trapping Rain Water in C#

using System;
// Trapping Rain Water in C#
//
// PURPOSE
// Two boundary maxima determine trapped water above each bar.
//
// METHOD
// Process the side with the smaller boundary maximum, because the opposite side already
// provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
// height.
//
// COMPLEXITY
// O(n) time, O(1) auxiliary space.
//
// CONTRACT
// Heights are nonnegative. Total volume must fit signed 32-bit.
// 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: 6.
// 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 trapped_water(ReadOnlySpan<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require((alg_value >= 0));
            }
            int left = 0;
            int right = (n - 1);
            int left_max = 0;
            int right_max = 0;
            int total = 0;
            while ((left <= right)) {
                if ((left_max <= right_max)) {
                    left_max = Math.Max(left_max, a[left]);
                    total = (total + (left_max - a[left]));
                    left = (left + 1);
                } else {
                    right_max = Math.Max(right_max, a[right]);
                    total = (total + (right_max - a[right]));
                    right = (right - 1);
                }
            }
            return total;
        }
    }

    static void Main() {
        int[] a = new int[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
        int result = trapped_water(a);
        Console.WriteLine(result);
    }
}