Kadane Maximum Subarray in Java

// Kadane Maximum Subarray in Java
//
// PURPOSE
// Kadane algorithm finds the largest sum of a contiguous nonempty subarray. At each
// position, a best ending subarray either extends the previous one or starts here.
//
// METHOD
// Track the best sum ending at the current position and the best seen anywhere. If extending
// is worse than restarting, start at the current value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// n >= 1. Returns the maximum sum, including the largest element when all values are
// negative. Sums must fit the integer type.
// 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: 6.
// 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 maximum_subarray(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require((n >= 1));
        int ending = a[0];
        int best = a[0];
        int i = 1;
        while ((i < n)) {
            ending = Math.max(a[i], Math.addExact(ending, a[i]));
            best = Math.max(best, ending);
            i = Math.addExact(i, 1);
        }
        return best;
    }

    public static void main(String[] args) {
        int[] a = new int[] {-2, 1, -3, 4, -1, 2, 1, -5, 4};
        int result = maximum_subarray(a);
        System.out.println(result);
    }
}