Binary Search in Java

// Binary Search in Java
//
// PURPOSE
// Binary search repeatedly halves a sorted search interval. It is useful when a large,
// sorted collection supports random access.
//
// METHOD
// Keep inclusive low and high bounds. Compare the middle element with target and discard the
// half that cannot contain it. The target, if present, remains inside the current interval.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// a must be sorted in ascending order; n is its length. Returns any matching index, or -1.
// The midpoint formula avoids adding two large indices.
// 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 binary_search(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));
        int lo = 0;
        int hi = Math.subtractExact(n, 1);
        int mid = 0;
        while ((lo <= hi)) {
            mid = Math.addExact(lo, (Math.subtractExact(hi, lo) / 2));
            if ((a[mid] == target)) {
                return mid;
            }
            if ((a[mid] < target)) {
                lo = Math.addExact(mid, 1);
            } else {
                hi = Math.subtractExact(mid, 1);
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 3, 5, 7};
        int target = 5;
        int result = binary_search(a, target);
        System.out.println(result);
    }
}