Matrix Chain Multiplication in Java

// Matrix Chain Multiplication in Java
//
// PURPOSE
// Matrix-chain DP chooses the parenthesization requiring the fewest scalar multiplications
// without changing matrix order.
//
// METHOD
// For each interval length, try every split and combine both subchain costs with the
// multiplication cost of their results.
//
// COMPLEXITY
// O(n cubed) time and O(n squared) space for n matrices.
//
// CONTRACT
// dimensions has n+1 positive entries; matrix i has dimensions[i] by dimensions[i+1]. n>=1.
// All candidate costs must be < 1000000000.
// 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: 4500.
// 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 matrix_chain(int[] dimensions) {
        java.util.Objects.requireNonNull(dimensions, "dimensions");
        int n = Math.subtractExact(dimensions.length, 1);
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((dimensions.length == Math.addExact(n, 1)));
        alg_require((n >= 1));
        for (int alg_i = 0; alg_i < dimensions.length; alg_i++) {
            int alg_value = dimensions[alg_i];
            alg_require(((alg_value > 0) && (alg_value <= 1000)));
        }
        int[] dp = new int[alg_size(Math.multiplyExact(n, n))];
        int length = 2;
        int left = 0;
        int right = 0;
        int split = 0;
        int candidate = 0;
        while ((length <= n)) {
            left = 0;
            while ((Math.addExact(left, length) <= n)) {
                right = Math.subtractExact(Math.addExact(left, length), 1);
                dp[Math.addExact(Math.multiplyExact(left, n), right)] = 1000000000;
                split = left;
                while ((split < right)) {
                    candidate = Math.addExact(Math.addExact(dp[Math.addExact(Math.multiplyExact(left, n), split)], dp[Math.addExact(Math.multiplyExact(Math.addExact(split, 1), n), right)]), Math.multiplyExact(Math.multiplyExact(dimensions[left], dimensions[Math.addExact(split, 1)]), dimensions[Math.addExact(right, 1)]));
                    dp[Math.addExact(Math.multiplyExact(left, n), right)] = Math.min(dp[Math.addExact(Math.multiplyExact(left, n), right)], candidate);
                    split = Math.addExact(split, 1);
                }
                left = Math.addExact(left, 1);
            }
            length = Math.addExact(length, 1);
        }
        return dp[Math.subtractExact(n, 1)];
    }

    public static void main(String[] args) {
        int[] dimensions = new int[] {10, 30, 5, 60};
        int result = matrix_chain(dimensions);
        System.out.println(result);
    }
}