Subset Sum Decision in Java

// Subset Sum Decision in Java
//
// PURPOSE
// Subset sum asks whether some selection of items totals an exact target. A reachability
// table records which sums can be formed.
//
// METHOD
// Mark zero reachable. For each item, scan sums downward and mark a sum reachable if it
// already was or if the sum minus the item was reachable before this item.
//
// COMPLEXITY
// O(n * target) time and O(target) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Items and target are nonnegative integers. Each input position can be used once. Returns 1
// if reachable, otherwise 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: 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 subset_sum(int[] a, int target) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require(((target >= 0) && (target <= 1000000)));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require((alg_value >= 0));
        }
        int[] dp = new int[alg_size(Math.addExact(target, 1))];
        dp[0] = 1;
        int i = 0;
        int s = 0;
        while ((i < n)) {
            s = target;
            while ((s >= a[i])) {
                if ((dp[Math.subtractExact(s, a[i])] != 0)) {
                    dp[s] = 1;
                }
                s = Math.subtractExact(s, 1);
            }
            i = Math.addExact(i, 1);
        }
        return dp[target];
    }

    public static void main(String[] args) {
        int[] a = new int[] {3, 4, 5};
        int target = 9;
        int result = subset_sum(a, target);
        System.out.println(result);
    }
}