Merge Based Inversion Count in Java

// Merge Based Inversion Count in Java
//
// PURPOSE
// An inversion is a pair i<j with a[i]>a[j]. Counting them during merging avoids testing
// every pair.
//
// METHOD
// Merge sorted runs bottom up. Whenever a right-run value precedes a larger left-run value,
// add the number of remaining left-run values.
//
// COMPLEXITY
// O(n log n) time, O(n) auxiliary space.
//
// CONTRACT
// Mutates input into sorted order. n <= 65536 so the inversion count fits signed 32-bit.
// 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.
// Expected a after call: [1, 2, 3].
// 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 inversion_count(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 <= 65536));
        int[] buffer = new int[alg_size(Math.addExact(n, 1))];
        int width = 1;
        int left = 0;
        int mid = 0;
        int right = 0;
        int i = 0;
        int j = 0;
        int out = 0;
        int count = 0;
        while ((width < n)) {
            left = 0;
            while ((left < n)) {
                mid = Math.min(Math.addExact(left, width), n);
                right = Math.min(Math.addExact(left, Math.multiplyExact(2, width)), n);
                i = left;
                j = mid;
                out = left;
                while ((out < right)) {
                    if (((i < mid) && ((j >= right) || (a[i] <= a[j])))) {
                        buffer[out] = a[i];
                        i = Math.addExact(i, 1);
                    } else {
                        buffer[out] = a[j];
                        j = Math.addExact(j, 1);
                        count = Math.addExact(count, Math.subtractExact(mid, i));
                    }
                    out = Math.addExact(out, 1);
                }
                left = Math.addExact(left, Math.multiplyExact(2, width));
            }
            i = 0;
            while ((i < n)) {
                a[i] = buffer[i];
                i = Math.addExact(i, 1);
            }
            width = Math.multiplyExact(width, 2);
        }
        return count;
    }

    public static void main(String[] args) {
        int[] a = new int[] {3, 1, 2};
        int result = inversion_count(a);
        System.out.println(result);
        // Expected a: [1, 2, 3]
        System.out.println(java.util.Arrays.toString(a));
    }
}