Z Algorithm in Java

// Z Algorithm in Java
//
// PURPOSE
// The Z array records how many tokens match the prefix at every position.
//
// METHOD
// Maintain the rightmost matching interval. Reuse a previously computed Z value when inside
// it, then extend only beyond its boundary.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned output.
//
// CONTRACT
// Integer token input; output has n entries. Defines Z[0]=0; 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 0.
// Expected output after call: [0, 2, 1, 0, 1].
// 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 z_array(int[] a, 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 == n));
        int left = 0;
        int right = 0;
        int i = 0;
        while ((i < n)) {
            output[i] = 0;
            i = Math.addExact(i, 1);
        }
        i = 1;
        while ((i < n)) {
            if ((i <= right)) {
                output[i] = Math.min(Math.addExact(Math.subtractExact(right, i), 1), output[Math.subtractExact(i, left)]);
            }
            while (((Math.addExact(i, output[i]) < n) && (a[output[i]] == a[Math.addExact(i, output[i])]))) {
                output[i] = Math.addExact(output[i], 1);
            }
            if ((Math.subtractExact(Math.addExact(i, output[i]), 1) > right)) {
                left = i;
                right = Math.subtractExact(Math.addExact(i, output[i]), 1);
            }
            i = Math.addExact(i, 1);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 1, 1, 2, 1};
        int[] output = new int[] {0, 0, 0, 0, 0};
        int result = z_array(a, output);
        System.out.println(result);
        // Expected output: [0, 2, 1, 0, 1]
        System.out.println(java.util.Arrays.toString(output));
    }
}