Interpolation Search in Java

// Interpolation Search in Java
//
// PURPOSE
// Interpolation search estimates the target position from endpoint values, which can help on
// roughly uniform numeric data.
//
// METHOD
// Estimate a position proportional to the target value between endpoint values. Compare
// there and discard the impossible side. Handle equal endpoints separately.
//
// COMPLEXITY
// Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
// O(1) space.
//
// CONTRACT
// Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
// signed 32-bit. Returns any 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: 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 interpolation_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));
        alg_require((n <= 10000));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require(((alg_value >= 0) && (alg_value <= 10000)));
        }
        int low = 0;
        int high = Math.subtractExact(n, 1);
        int pos = 0;
        while (((low <= high) && (target >= a[low]) && (target <= a[high]))) {
            if ((a[low] == a[high])) {
                return low;
            }
            pos = Math.addExact(low, (Math.multiplyExact(Math.subtractExact(target, a[low]), Math.subtractExact(high, low)) / Math.subtractExact(a[high], a[low])));
            if ((a[pos] == target)) {
                return pos;
            }
            if ((a[pos] < target)) {
                low = Math.addExact(pos, 1);
            } else {
                high = Math.subtractExact(pos, 1);
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] a = new int[] {0, 10, 20, 30};
        int target = 20;
        int result = interpolation_search(a, target);
        System.out.println(result);
    }
}