DAG Shortest Path in Java

// DAG Shortest Path in Java
//
// PURPOSE
// A directed acyclic graph permits shortest-path relaxation in topological order even when
// weights are negative.
//
// METHOD
// Use Kahn ordering and relax each outgoing edge when removing its source. Detect a cycle if
// not all vertices are processed.
//
// COMPLEXITY
// O(n squared) time with a dense matrix and O(n) auxiliary space.
//
// CONTRACT
// Flattened matrix uses INF=1000000000 for missing edges. Diagonal must be INF (no self-
// loops). Finite sums stay strictly between -INF and INF. Returns INF if unreachable, -INF
// if cyclic.
// 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: 2.
// 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 dag_shortest_path(int[] graph, int n, int source, int target) {
        java.util.Objects.requireNonNull(graph, "graph");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((graph.length == Math.multiplyExact(n, n)));
        alg_require(((n >= 1) && (source >= 0) && (source < n)));
        alg_require(((target >= 0) && (target < n)));
        int[] degree = new int[alg_size(n)];
        int[] distance = new int[alg_size(n)];
        int[] queue = new int[alg_size(n)];
        int head = 0;
        int tail = 0;
        int u = 0;
        int v = 0;
        while ((u < n)) {
            distance[u] = 1000000000;
            v = 0;
            while ((v < n)) {
                if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 1000000000)) {
                    degree[v] = Math.addExact(degree[v], 1);
                }
                v = Math.addExact(v, 1);
            }
            u = Math.addExact(u, 1);
        }
        distance[source] = 0;
        v = 0;
        while ((v < n)) {
            if ((degree[v] == 0)) {
                queue[tail] = v;
                tail = Math.addExact(tail, 1);
            }
            v = Math.addExact(v, 1);
        }
        while ((head < tail)) {
            u = queue[head];
            head = Math.addExact(head, 1);
            v = 0;
            while ((v < n)) {
                if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] != 1000000000)) {
                    if ((distance[u] != 1000000000)) {
                        distance[v] = Math.min(distance[v], Math.addExact(distance[u], graph[Math.addExact(Math.multiplyExact(u, n), v)]));
                    }
                    degree[v] = Math.subtractExact(degree[v], 1);
                    if ((degree[v] == 0)) {
                        queue[tail] = v;
                        tail = Math.addExact(tail, 1);
                    }
                }
                v = Math.addExact(v, 1);
            }
        }
        if ((tail != n)) {
            return Math.negateExact(1000000000);
        }
        return distance[target];
    }

    public static void main(String[] args) {
        int[] graph = new int[] {1000000000, 4, 10, 1000000000, 1000000000, -2, 1000000000, 1000000000, 1000000000};
        int n = 3;
        int source = 0;
        int target = 2;
        int result = dag_shortest_path(graph, n, source, target);
        System.out.println(result);
    }
}