Disjoint Set Union in Java

// Disjoint Set Union in Java
//
// PURPOSE
// Disjoint set union maintains connected components as a forest of parent links. Union by
// size and path compression keep repeated operations nearly constant in amortized time.
//
// METHOD
// Start with each vertex as its own component. Find each edge endpoint root with path
// halving. If roots differ, attach the smaller tree to the larger and decrease the component
// count.
//
// COMPLEXITY
// O(n + m alpha(n)) amortized time and O(n) auxiliary space, where alpha is the inverse
// Ackermann function.
//
// CONTRACT
// n >= 0; edge arrays u_edges and v_edges have m valid vertex indices each. Treats edges as
// undirected. Returns component count; isolated vertices count separately.
// 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 component_count(int[] u_edges, int[] v_edges, int n) {
        java.util.Objects.requireNonNull(u_edges, "u_edges");
        java.util.Objects.requireNonNull(v_edges, "v_edges");
        int m = u_edges.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((m >= 0) && (m <= 1000000)));
        alg_require((u_edges.length == m));
        alg_require((v_edges.length == m));
        for (int alg_i = 0; alg_i < u_edges.length; alg_i++) {
            int alg_value = u_edges[alg_i];
            alg_require(((alg_value >= 0) && (alg_value < n)));
        }
        for (int alg_i = 0; alg_i < v_edges.length; alg_i++) {
            int alg_value = v_edges[alg_i];
            alg_require(((alg_value >= 0) && (alg_value < n)));
        }
        int[] parent = new int[alg_size(Math.addExact(n, 1))];
        int[] size = new int[alg_size(Math.addExact(n, 1))];
        int i = 0;
        int edge = 0;
        int u = 0;
        int v = 0;
        int temp = 0;
        int count = n;
        while ((i < n)) {
            parent[i] = i;
            size[i] = 1;
            i = Math.addExact(i, 1);
        }
        while ((edge < m)) {
            u = u_edges[edge];
            v = v_edges[edge];
            while ((parent[u] != u)) {
                parent[u] = parent[parent[u]];
                u = parent[u];
            }
            while ((parent[v] != v)) {
                parent[v] = parent[parent[v]];
                v = parent[v];
            }
            if ((u != v)) {
                if ((size[u] < size[v])) {
                    temp = u;
                    u = v;
                    v = temp;
                }
                parent[v] = u;
                size[u] = Math.addExact(size[u], size[v]);
                count = Math.subtractExact(count, 1);
            }
            edge = Math.addExact(edge, 1);
        }
        return count;
    }

    public static void main(String[] args) {
        int[] u_edges = new int[] {0, 1, 3};
        int[] v_edges = new int[] {1, 2, 4};
        int n = 5;
        int result = component_count(u_edges, v_edges, n);
        System.out.println(result);
    }
}