Prefix Sum Range Query in C#

using System;
// Prefix Sum Range Query in C#
//
// PURPOSE
// Prefix sums turn a range sum into a subtraction. The preprocessed prefix at index i stores
// the sum of all elements before i.
//
// METHOD
// Build prefix[i+1] = prefix[i] + a[i]. For inclusive bounds left and right, subtract
// prefix[left] from prefix[right+1]. Build once and reuse the prefix for many queries in a
// real application.
//
// COMPLEXITY
// O(n) preprocessing and O(n) space; each query after preprocessing is O(1). This self-
// contained function includes preprocessing on every call.
//
// CONTRACT
// 0 <= left <= right < n. Returns the inclusive range sum. All prefix totals 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: 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 range_sum(ReadOnlySpan<int> a, int left, int right) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require(((left >= 0) && (left <= right) && (right < n)));
            int[] prefix = new int[alg_size((n + 1))];
            int i = 0;
            while ((i < n)) {
                prefix[(i + 1)] = (prefix[i] + a[i]);
                i = (i + 1);
            }
            return (prefix[(right + 1)] - prefix[left]);
        }
    }

    static void Main() {
        int[] a = new int[] {2, 4, -1, 3};
        int left = 1;
        int right = 3;
        int result = range_sum(a, left, right);
        Console.WriteLine(result);
    }
}