Prefix Sum Range Query in Java

// Prefix Sum Range Query in Java
//
// PURPOSE
// Prefix sums turn a range sum into a subtraction. The preprocessed prefix at index i stores
// the sum of all elements before i.
//
// METHOD
// Build prefix[i+1] = prefix[i] + a[i]. For inclusive bounds left and right, subtract
// prefix[left] from prefix[right+1]. Build once and reuse the prefix for many queries in a
// real application.
//
// COMPLEXITY
// O(n) preprocessing and O(n) space; each query after preprocessing is O(1). This self-
// contained function includes preprocessing on every call.
//
// CONTRACT
// 0 <= left <= right < n. Returns the inclusive range sum. All prefix totals must fit.
// 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: 6.
// 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 range_sum(int[] a, int left, int right) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require(((left >= 0) && (left <= right) && (right < n)));
        int[] prefix = new int[alg_size(Math.addExact(n, 1))];
        int i = 0;
        while ((i < n)) {
            prefix[Math.addExact(i, 1)] = Math.addExact(prefix[i], a[i]);
            i = Math.addExact(i, 1);
        }
        return Math.subtractExact(prefix[Math.addExact(right, 1)], prefix[left]);
    }

    public static void main(String[] args) {
        int[] a = new int[] {2, 4, -1, 3};
        int left = 1;
        int right = 3;
        int result = range_sum(a, left, right);
        System.out.println(result);
    }
}