Longest Common Subsequence in Java

// Longest Common Subsequence in Java
//
// PURPOSE
// LCS finds the longest sequence appearing in two inputs in the same order, with gaps
// allowed. It is a foundation for comparison tools.
//
// METHOD
// Use one row of prefix lengths and retain the previous diagonal in a scalar. Equal tokens
// extend the diagonal; otherwise choose the best result from above or left.
//
// COMPLEXITY
// O(nm) time and O(min(n,m)) auxiliary space. The public function automatically orients the
// shorter input as its work row.
//
// CONTRACT
// Inputs are integer token sequences. Returns length only. Empty inputs are valid. Only one
// row of the dynamic program is retained.
// 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: 2.
// 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 lcs_length(int[] a, int[] b) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(b, "b");
        int n = a.length;
        int m = b.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((m >= 0) && (m <= 1000000)));
        alg_require((a.length == n));
        alg_require((b.length == m));
        if (n < m) return lcs_length(b, a);
        int[] dp = new int[alg_size(Math.addExact(m, 1))];
        int i = 0;
        int j = 0;
        int diagonal = 0;
        int old = 0;
        while ((i < n)) {
            diagonal = 0;
            j = 1;
            while ((j <= m)) {
                old = dp[j];
                if ((a[i] == b[Math.subtractExact(j, 1)])) {
                    dp[j] = Math.addExact(diagonal, 1);
                } else {
                    dp[j] = Math.max(dp[j], dp[Math.subtractExact(j, 1)]);
                }
                diagonal = old;
                j = Math.addExact(j, 1);
            }
            i = Math.addExact(i, 1);
        }
        return dp[m];
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 3};
        int[] b = new int[] {2, 3, 4};
        int result = lcs_length(a, b);
        System.out.println(result);
    }
}