Iterative Segment Tree Build in C#

using System;
// Iterative Segment Tree Build in C#
//
// PURPOSE
// An iterative sum segment tree stores leaves in the second half of a flat array and parents
// in the first half.
//
// METHOD
// Copy values into tree[n+i], then compute every internal node from its two children in
// descending index order.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// n>=1, tree length is 2*n. Build once and reuse for point assignments and half-open range
// queries. Sums 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: 0.
// Expected tree after call: [0, 10, 3, 7, 1, 2, 3, 4].
// 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 segment_build(ReadOnlySpan<int> a, Span<int> tree) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require((tree.Length == (2 * n)));
            alg_require((n >= 1));
            int i = 0;
            tree[0] = 0;
            while ((i < n)) {
                tree[(n + i)] = a[i];
                i = (i + 1);
            }
            i = (n - 1);
            while ((i > 0)) {
                tree[i] = (tree[(2 * i)] + tree[((2 * i) + 1)]);
                i = (i - 1);
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {1, 2, 3, 4};
        int[] tree = new int[] {0, 0, 0, 0, 0, 0, 0, 0};
        int result = segment_build(a, tree);
        Console.WriteLine(result);
        // Expected tree: [0, 10, 3, 7, 1, 2, 3, 4]
        Console.WriteLine("[" + string.Join(", ", tree) + "]");
    }
}