Jump Search in Java

// Jump Search in Java
//
// PURPOSE
// Jump search skips fixed-size blocks in a sorted sequence, then scans the candidate block.
//
// METHOD
// Choose a block width near square root of n. Jump until the block endpoint is at least the
// target, then scan the block.
//
// COMPLEXITY
// O(sqrt(n)) comparisons and O(1) auxiliary space. Binary search is usually faster on
// random-access arrays.
//
// CONTRACT
// Ascending input; returns first matching index or -1.
// 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 jump_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 step = 1;
        while ((step <= (n / step))) {
            step = Math.addExact(step, 1);
        }
        int start = 0;
        int end = Math.min(step, n);
        while (((start < n) && (a[Math.subtractExact(end, 1)] < target))) {
            start = end;
            end = Math.min(Math.addExact(end, step), n);
        }
        while ((start < end)) {
            if ((a[start] == target)) {
                return start;
            }
            start = Math.addExact(start, 1);
        }
        return Math.negateExact(1);
    }

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