Fenwick Tree Linear Build in C#

using System;
// Fenwick Tree Linear Build in C#
//
// PURPOSE
// A Fenwick tree stores partial sums so point additions and prefix queries take logarithmic
// time.
//
// METHOD
// Copy each value into its one-based tree position, then propagate the completed partial sum
// to its Fenwick parent. Each node is propagated only once.
//
// COMPLEXITY
// O(n) build time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// tree has n+1 entries. Overwrites tree; sums fit signed 32-bit. Build once, then reuse with
// Fenwick Point Add and Fenwick Prefix Sum.
// 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, 1, 3, 3, 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 fenwick_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 == (n + 1)));
            int i = 0;
            int parent = 0;
            while ((i <= n)) {
                tree[i] = 0;
                i = (i + 1);
            }
            i = 1;
            while ((i <= n)) {
                tree[i] = (tree[i] + a[(i - 1)]);
                parent = (i + (i & (-i)));
                if ((parent <= n)) {
                    tree[parent] = (tree[parent] + tree[i]);
                }
                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};
        int result = fenwick_build(a, tree);
        Console.WriteLine(result);
        // Expected tree: [0, 1, 3, 3, 10]
        Console.WriteLine("[" + string.Join(", ", tree) + "]");
    }
}