Longest Palindromic Subsequence in Java

// Longest Palindromic Subsequence in Java
//
// PURPOSE
// A longest palindromic subsequence may skip tokens while preserving order. It differs from
// a contiguous palindromic substring.
//
// METHOD
// Scan left endpoints backward and right endpoints forward. Equal endpoints extend the inner
// solution by two; otherwise discard one endpoint. Retain one row and the old diagonal.
//
// COMPLEXITY
// O(n squared) time, O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns length; 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 5.
// 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 palindromic_subsequence(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int[] dp = new int[alg_size(Math.addExact(n, 1))];
        int left = Math.subtractExact(n, 1);
        int right = 0;
        int diagonal = 0;
        int old = 0;
        while ((left >= 0)) {
            dp[left] = 1;
            diagonal = 0;
            right = Math.addExact(left, 1);
            while ((right < n)) {
                old = dp[right];
                if ((a[left] == a[right])) {
                    dp[right] = Math.addExact(diagonal, 2);
                } else {
                    dp[right] = Math.max(dp[right], dp[Math.subtractExact(right, 1)]);
                }
                diagonal = old;
                right = Math.addExact(right, 1);
            }
            left = Math.subtractExact(left, 1);
        }
        if ((n == 0)) {
            return 0;
        }
        return dp[Math.subtractExact(n, 1)];
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 3, 2, 1};
        int result = palindromic_subsequence(a);
        System.out.println(result);
    }
}