Boyer Moore Majority Vote in Java

// Boyer Moore Majority Vote in Java
//
// PURPOSE
// Majority vote cancels pairs of different values. If a value occurs more than half the
// time, it survives as the final candidate.
//
// METHOD
// Choose a new candidate whenever the balance is zero. Increment for matching values and
// decrement for different ones. Make a second pass to verify the candidate, since a majority
// need not exist.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space.
//
// CONTRACT
// Returns the INDEX of a verified majority value, or -1 if none exists. Returning an index
// avoids colliding with any valid integer value.
// 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: 0.
// 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 majority_index(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int candidate = 0;
        int balance = 0;
        int i = 0;
        int count = 0;
        while ((i < n)) {
            if ((balance == 0)) {
                candidate = i;
            }
            if ((a[i] == a[candidate])) {
                balance = Math.addExact(balance, 1);
            } else {
                balance = Math.subtractExact(balance, 1);
            }
            i = Math.addExact(i, 1);
        }
        i = 0;
        while ((i < n)) {
            if ((a[i] == a[candidate])) {
                count = Math.addExact(count, 1);
            }
            i = Math.addExact(i, 1);
        }
        if ((count > (n / 2))) {
            return candidate;
        }
        return Math.negateExact(1);
    }

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