Monotonic Deque Sliding Maximum in Java

// Monotonic Deque Sliding Maximum in Java
//
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 6.
// Expected output after call: [3, 3, 5, 5, 6, 7].
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int sliding_maximum(int[] a, int k, int[] output) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(output, "output");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require((output.length == Math.addExact(Math.subtractExact(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] <= Math.subtractExact(i, k)))) {
                head = Math.addExact(head, 1);
            }
            while (((head < tail) && (a[queue[Math.subtractExact(tail, 1)]] <= a[i]))) {
                tail = Math.subtractExact(tail, 1);
            }
            queue[tail] = i;
            tail = Math.addExact(tail, 1);
            if ((i >= Math.subtractExact(k, 1))) {
                output[Math.addExact(Math.subtractExact(i, k), 1)] = a[queue[head]];
            }
            i = Math.addExact(i, 1);
        }
        return Math.addExact(Math.subtractExact(n, k), 1);
    }

    public static void main(String[] args) {
        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);
        System.out.println(result);
        // Expected output: [3, 3, 5, 5, 6, 7]
        System.out.println(java.util.Arrays.toString(output));
    }
}