Iterative Segment Tree Range Sum in Java

// Iterative Segment Tree Range Sum in Java
//
// PURPOSE
// A segment tree range query combines the small number of disjoint nodes covering a half-
// open interval.
//
// METHOD
// Move both endpoints to leaves. Include a left endpoint when it is a right child and a
// right endpoint when it is about to cross a left child, then move both up.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree has 2*n entries; n>=1, 0<=left<=right<=n. Returns sum in [left,right). Empty range
// returns zero.
// 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: 5.
// 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 segment_sum(int[] tree, int left, int right) {
        java.util.Objects.requireNonNull(tree, "tree");
        int n = (tree.length / 2);
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((tree.length == Math.multiplyExact(2, n)));
        alg_require(((n >= 1) && (left >= 0) && (left <= right) && (right <= n)));
        left = Math.addExact(left, n);
        right = Math.addExact(right, n);
        int total = 0;
        while ((left < right)) {
            if (((left % 2) == 1)) {
                total = Math.addExact(total, tree[left]);
                left = Math.addExact(left, 1);
            }
            if (((right % 2) == 1)) {
                right = Math.subtractExact(right, 1);
                total = Math.addExact(total, tree[right]);
            }
            left = (left / 2);
            right = (right / 2);
        }
        return total;
    }

    public static void main(String[] args) {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int left = 1;
        int right = 3;
        int result = segment_sum(tree, left, right);
        System.out.println(result);
    }
}