Longest Increasing Subsequence in C#

using System;
// Longest Increasing Subsequence in C#
//
// PURPOSE
// Patience-style tail tracking finds the length of a longest strictly increasing subsequence
// using binary search. A subsequence may skip elements while preserving order.
//
// METHOD
// Keep the smallest possible tail for each subsequence length. Lower-bound search finds the
// first tail at least as large as the next value. Replace that tail or extend the length.
// Strict increase means equal values replace rather than extend.
//
// COMPLEXITY
// O(n log n) time and O(n) auxiliary space.
//
// CONTRACT
// Returns the length only. Equal values do not extend a strictly increasing subsequence.
// Empty input 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: 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 lis_length(ReadOnlySpan<int> a) {
        int n = a.Length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.Length == n));
        int[] tails = new int[a.Length];
        int length = 0;
        foreach (int value in a) {
            int at = Array.BinarySearch(tails, 0, length, value);
            if (at < 0) at = ~at;
            tails[at] = value;
            if (at == length) length++;
        }
        return length;
    }

    static void Main() {
        int[] a = new int[] {10, 9, 2, 5, 3, 7, 101, 18};
        int result = lis_length(a);
        Console.WriteLine(result);
    }
}