Trapping Rain Water in Java

// Trapping Rain Water in Java
//
// PURPOSE
// Two boundary maxima determine trapped water above each bar.
//
// METHOD
// Process the side with the smaller boundary maximum, because the opposite side already
// provides a sufficiently high boundary. Accumulate that side's maximum minus its bar
// height.
//
// COMPLEXITY
// O(n) time, O(1) auxiliary space.
//
// CONTRACT
// Heights are nonnegative. Total volume must fit 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: 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 trapped_water(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require((alg_value >= 0));
        }
        int left = 0;
        int right = Math.subtractExact(n, 1);
        int left_max = 0;
        int right_max = 0;
        int total = 0;
        while ((left <= right)) {
            if ((left_max <= right_max)) {
                left_max = Math.max(left_max, a[left]);
                total = Math.addExact(total, Math.subtractExact(left_max, a[left]));
                left = Math.addExact(left, 1);
            } else {
                right_max = Math.max(right_max, a[right]);
                total = Math.addExact(total, Math.subtractExact(right_max, a[right]));
                right = Math.subtractExact(right, 1);
            }
        }
        return total;
    }

    public static void main(String[] args) {
        int[] a = new int[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
        int result = trapped_water(a);
        System.out.println(result);
    }
}