Manacher Longest Palindromic Substring in Java

// Manacher Longest Palindromic Substring in Java
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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: 4.
// 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 manacher(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int[] radius = new int[alg_size(Math.addExact(n, 1))];
        int parity = 0;
        int left = 0;
        int right = Math.negateExact(1);
        int i = 0;
        int k = 0;
        int best = 0;
        while ((parity < 2)) {
            left = 0;
            right = Math.negateExact(1);
            i = 0;
            while ((i < n)) {
                k = Math.subtractExact(1, parity);
                if ((i <= right)) {
                    k = Math.min(radius[Math.addExact(Math.subtractExact(Math.addExact(left, right), i), parity)], Math.addExact(Math.subtractExact(right, i), 1));
                }
                while (((Math.subtractExact(Math.subtractExact(i, k), parity) >= 0) && (Math.addExact(i, k) < n) && (a[Math.subtractExact(Math.subtractExact(i, k), parity)] == a[Math.addExact(i, k)]))) {
                    k = Math.addExact(k, 1);
                }
                radius[i] = k;
                best = Math.max(best, Math.addExact(Math.subtractExact(Math.multiplyExact(2, k), 1), parity));
                if ((Math.subtractExact(Math.addExact(i, k), 1) > right)) {
                    left = Math.addExact(Math.subtractExact(Math.subtractExact(i, k), parity), 1);
                    right = Math.subtractExact(Math.addExact(i, k), 1);
                }
                i = Math.addExact(i, 1);
            }
            parity = Math.addExact(parity, 1);
        }
        return best;
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 2, 1};
        int result = manacher(a);
        System.out.println(result);
    }
}