Iterative Segment Tree Point Assignment in C#

using System;
// Iterative Segment Tree Point Assignment in C#
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// returns 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: 0.
// Expected tree after call: [0, 17, 10, 7, 1, 9, 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_set(Span<int> tree, int index, int value) {
        checked {
            int n = (tree.Length / 2);
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((tree.Length == (2 * n)));
            alg_require(((n >= 1) && (index >= 0) && (index < n)));
            index = (index + n);
            tree[index] = value;
            index = (index / 2);
            while ((index > 0)) {
                tree[index] = (tree[(2 * index)] + tree[((2 * index) + 1)]);
                index = (index / 2);
            }
            return 0;
        }
    }

    static void Main() {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int index = 1;
        int value = 9;
        int result = segment_set(tree, index, value);
        Console.WriteLine(result);
        // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
        Console.WriteLine("[" + string.Join(", ", tree) + "]");
    }
}