Merge Based Inversion Count in C#

using System;
// Merge Based Inversion Count in C#
//
// PURPOSE
// An inversion is a pair i<j with a[i]>a[j]. Counting them during merging avoids testing
// every pair.
//
// METHOD
// Merge sorted runs bottom up. Whenever a right-run value precedes a larger left-run value,
// add the number of remaining left-run values.
//
// COMPLEXITY
// O(n log n) time, O(n) auxiliary space.
//
// CONTRACT
// Mutates input into sorted order. n <= 65536 so the inversion count fits 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: 2.
// Expected a after call: [1, 2, 3].
// 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 inversion_count(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require((n <= 65536));
            int[] buffer = new int[alg_size((n + 1))];
            int width = 1;
            int left = 0;
            int mid = 0;
            int right = 0;
            int i = 0;
            int j = 0;
            int out_value = 0;
            int count = 0;
            while ((width < n)) {
                left = 0;
                while ((left < n)) {
                    mid = Math.Min((left + width), n);
                    right = Math.Min((left + (2 * width)), n);
                    i = left;
                    j = mid;
                    out_value = left;
                    while ((out_value < right)) {
                        if (((i < mid) && ((j >= right) || (a[i] <= a[j])))) {
                            buffer[out_value] = a[i];
                            i = (i + 1);
                        } else {
                            buffer[out_value] = a[j];
                            j = (j + 1);
                            count = (count + (mid - i));
                        }
                        out_value = (out_value + 1);
                    }
                    left = (left + (2 * width));
                }
                i = 0;
                while ((i < n)) {
                    a[i] = buffer[i];
                    i = (i + 1);
                }
                width = (width * 2);
            }
            return count;
        }
    }

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