Rod Cutting in Java

// Rod Cutting in Java
//
// PURPOSE
// Rod cutting chooses cuts that maximize the sale value of a rod. It considers every first
// piece and reuses the optimal solution for the remaining length.
//
// METHOD
// Set the value of length zero to zero. For each length, try each possible first cut and
// combine its price with the already computed remainder value.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space.
//
// CONTRACT
// prices[i] is the nonnegative price for length i+1 and contains n entries. Returns maximum
// revenue for length n. Revenue 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: 10.
// 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 rod_cutting(int[] prices, int n) {
        java.util.Objects.requireNonNull(prices, "prices");
        alg_require(((n >= 0) && (n <= 1000000)));
        int[] dp = new int[alg_size(Math.addExact(n, 1))];
        int length = 1;
        int cut = 0;
        while ((length <= n)) {
            cut = 1;
            while ((cut <= length)) {
                dp[length] = Math.max(dp[length], Math.addExact(prices[Math.subtractExact(cut, 1)], dp[Math.subtractExact(length, cut)]));
                cut = Math.addExact(cut, 1);
            }
            length = Math.addExact(length, 1);
        }
        return dp[n];
    }

    public static void main(String[] args) {
        int[] prices = new int[] {1, 5, 8, 9};
        int n = 4;
        int result = rod_cutting(prices, n);
        System.out.println(result);
    }
}