Levenshtein Edit Distance in C#

using System;
// Levenshtein Edit Distance in C#
//
// PURPOSE
// Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed
// to turn one token sequence into another.
//
// METHOD
// Retain one row and the previous diagonal. Equal tokens keep the diagonal distance.
// Different tokens add one to the cheapest deletion, insertion, or substitution.
//
// COMPLEXITY
// O(nm) time and O(min(n,m)) auxiliary space. The public function automatically orients the
// shorter input as its work row.
//
// CONTRACT
// Inputs are integer tokens. For text, tokenize consistently before calling; Unicode
// normalization and grapheme rules are separate concerns. Returns distance only.
// 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.
// 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 edit_distance(ReadOnlySpan<int> a, ReadOnlySpan<int> b) {
        checked {
            int n = a.Length;
            int m = b.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((m >= 0) && (m <= 1000000)));
            alg_require((a.Length == n));
            alg_require((b.Length == m));
            if (n < m) return edit_distance(b, a);
            int[] dp = new int[alg_size((m + 1))];
            int i = 0;
            int j = 0;
            int diagonal = 0;
            int old = 0;
            while ((j <= m)) {
                dp[j] = j;
                j = (j + 1);
            }
            while ((i < n)) {
                diagonal = dp[0];
                dp[0] = (i + 1);
                j = 1;
                while ((j <= m)) {
                    old = dp[j];
                    if ((a[i] == b[(j - 1)])) {
                        dp[j] = diagonal;
                    } else {
                        dp[j] = (1 + Math.Min(dp[j], Math.Min(dp[(j - 1)], diagonal)));
                    }
                    diagonal = old;
                    j = (j + 1);
                }
                i = (i + 1);
            }
            return dp[m];
        }
    }

    static void Main() {
        int[] a = new int[] {1, 2, 3};
        int[] b = new int[] {1, 4, 3, 5};
        int result = edit_distance(a, b);
        Console.WriteLine(result);
    }
}