Monotonic Deque Sliding Maximum in C#

using System;
// Monotonic Deque Sliding Maximum in C#
//
// PURPOSE
// A monotonic deque returns every fixed-window maximum in linear time.
//
// METHOD
// Keep candidate indices in decreasing value order. Discard expired indices from the front
// and dominated candidates from the back; the front is the current maximum.
//
// COMPLEXITY
// O(n) time; O(n) allocated index-buffer space in this linear-buffer implementation, with at
// most k live candidates.
//
// CONTRACT
// 1 <= k <= n. output has n-k+1 entries. Writes maximum values and returns output length.
// 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.
// Expected output after call: [3, 3, 5, 5, 6, 7].
// 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 sliding_maximum(ReadOnlySpan<int> a, int k, Span<int> output) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require((output.Length == ((n - k) + 1)));
            alg_require(((k >= 1) && (k <= n)));
            int[] queue = new int[alg_size(n)];
            int head = 0;
            int tail = 0;
            int i = 0;
            while ((i < n)) {
                while (((head < tail) && (queue[head] <= (i - k)))) {
                    head = (head + 1);
                }
                while (((head < tail) && (a[queue[(tail - 1)]] <= a[i]))) {
                    tail = (tail - 1);
                }
                queue[tail] = i;
                tail = (tail + 1);
                if ((i >= (k - 1))) {
                    output[((i - k) + 1)] = a[queue[head]];
                }
                i = (i + 1);
            }
            return ((n - k) + 1);
        }
    }

    static void Main() {
        int[] a = new int[] {1, 3, -1, -3, 5, 3, 6, 7};
        int k = 3;
        int[] output = new int[] {0, 0, 0, 0, 0, 0};
        int result = sliding_maximum(a, k, output);
        Console.WriteLine(result);
        // Expected output: [3, 3, 5, 5, 6, 7]
        Console.WriteLine("[" + string.Join(", ", output) + "]");
    }
}