0-1 Knapsack in Java

// 0-1 Knapsack in Java
//
// PURPOSE
// Knapsack chooses items with maximum total value under a weight limit, using each item at
// most once. The one-dimensional table stores the best value for each capacity.
//
// METHOD
// Process items one at a time and capacities downward. Compare skipping the item with adding
// its value to the previous best at the remaining capacity. Descending capacities prevent
// reusing the current item.
//
// COMPLEXITY
// O(n * capacity) time and O(capacity) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Weights are positive, values nonnegative, capacity >= 0. Both arrays have n entries.
// Returns best value, not the chosen item set.
// 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: 9.
// 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 knapsack(int[] weights, int[] values, int capacity) {
        java.util.Objects.requireNonNull(weights, "weights");
        java.util.Objects.requireNonNull(values, "values");
        int n = weights.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((weights.length == n));
        alg_require((values.length == n));
        alg_require(((capacity >= 0) && (capacity <= 1000000)));
        for (int alg_i = 0; alg_i < weights.length; alg_i++) {
            int alg_value = weights[alg_i];
            alg_require((alg_value > 0));
        }
        for (int alg_i = 0; alg_i < values.length; alg_i++) {
            int alg_value = values[alg_i];
            alg_require((alg_value >= 0));
        }
        int[] dp = new int[alg_size(Math.addExact(capacity, 1))];
        int i = 0;
        int c = 0;
        while ((i < n)) {
            c = capacity;
            while ((c >= weights[i])) {
                dp[c] = Math.max(dp[c], Math.addExact(dp[Math.subtractExact(c, weights[i])], values[i]));
                c = Math.subtractExact(c, 1);
            }
            i = Math.addExact(i, 1);
        }
        return dp[capacity];
    }

    public static void main(String[] args) {
        int[] weights = new int[] {2, 3, 4};
        int[] values = new int[] {4, 5, 7};
        int capacity = 5;
        int result = knapsack(weights, values, capacity);
        System.out.println(result);
    }
}