Iterative Segment Tree Point Assignment in Java

// Iterative Segment Tree Point Assignment in Java
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// returns 0.
// 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: 0.
// Expected tree after call: [0, 17, 10, 7, 1, 9, 3, 4].
// 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_set(int[] tree, int index, int value) {
        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) && (index >= 0) && (index < n)));
        index = Math.addExact(index, n);
        tree[index] = value;
        index = (index / 2);
        while ((index > 0)) {
            tree[index] = Math.addExact(tree[Math.multiplyExact(2, index)], tree[Math.addExact(Math.multiplyExact(2, index), 1)]);
            index = (index / 2);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int index = 1;
        int value = 9;
        int result = segment_set(tree, index, value);
        System.out.println(result);
        // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
        System.out.println(java.util.Arrays.toString(tree));
    }
}