Prim Minimum Spanning Tree in Java

// Prim Minimum Spanning Tree in Java
//
// PURPOSE
// Prim grows a minimum spanning tree by choosing the cheapest edge that connects an
// unvisited vertex to the current tree. The cut property justifies each greedy choice.
//
// METHOD
// Keep the cheapest connection cost for every unvisited vertex. Select the cheapest one, add
// its cost, and update neighbors. If no finite connection remains before all vertices are
// added, the graph is disconnected.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space for a dense adjacency matrix.
//
// CONTRACT
// n >= 1; symmetric flattened matrix for an undirected graph. -1 means absent, weights are
// nonnegative and < 1,000,000,000. Total must fit. Returns MST weight or -1 if disconnected.
// 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 prim_mst(int[] graph, int n) {
        java.util.Objects.requireNonNull(graph, "graph");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((graph.length == Math.multiplyExact(n, n)));
        alg_require((n >= 1));
        for (int alg_i = 0; alg_i < graph.length; alg_i++) {
            int alg_value = graph[alg_i];
            alg_require(((alg_value >= Math.negateExact(1)) && (alg_value < 1000000000)));
        }
        int[] cost = new int[alg_size(n)];
        int[] used = new int[alg_size(n)];
        int i = 0;
        int v = 0;
        int u = 0;
        int best = 0;
        int total = 0;
        while ((i < n)) {
            cost[i] = 1000000000;
            i = Math.addExact(i, 1);
        }
        cost[0] = 0;
        i = 0;
        while ((i < n)) {
            u = Math.negateExact(1);
            best = 1000000000;
            v = 0;
            while ((v < n)) {
                if (((used[v] == 0) && (cost[v] < best))) {
                    best = cost[v];
                    u = v;
                }
                v = Math.addExact(v, 1);
            }
            if ((u == Math.negateExact(1))) {
                return Math.negateExact(1);
            }
            used[u] = 1;
            total = Math.addExact(total, cost[u]);
            v = 0;
            while ((v < n)) {
                if ((graph[Math.addExact(Math.multiplyExact(u, n), v)] >= 0)) {
                    cost[v] = Math.min(cost[v], graph[Math.addExact(Math.multiplyExact(u, n), v)]);
                }
                v = Math.addExact(v, 1);
            }
            i = Math.addExact(i, 1);
        }
        return total;
    }

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