Iterative Segment Tree Build in Java

// Iterative Segment Tree Build in Java
//
// PURPOSE
// An iterative sum segment tree stores leaves in the second half of a flat array and parents
// in the first half.
//
// METHOD
// Copy values into tree[n+i], then compute every internal node from its two children in
// descending index order.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// n>=1, tree length is 2*n. Build once and reuse for point assignments and half-open range
// queries. Sums 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: 0.
// Expected tree after call: [0, 10, 3, 7, 1, 2, 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_build(int[] a, int[] tree) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(tree, "tree");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require((tree.length == Math.multiplyExact(2, n)));
        alg_require((n >= 1));
        int i = 0;
        tree[0] = 0;
        while ((i < n)) {
            tree[Math.addExact(n, i)] = a[i];
            i = Math.addExact(i, 1);
        }
        i = Math.subtractExact(n, 1);
        while ((i > 0)) {
            tree[i] = Math.addExact(tree[Math.multiplyExact(2, i)], tree[Math.addExact(Math.multiplyExact(2, i), 1)]);
            i = Math.subtractExact(i, 1);
        }
        return 0;
    }

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