java-topology/tests/support/TopoSorterAlgorithm.java

package support;

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

/**
 * Reference implementations of ModuleHashesBuilder$TopoSorter.visit() — defective and fixed.
 *
 * DEFECT 0003 (java.base/jdk.internal.module): visit() checks
 * Deque.contains(node) to detect whether the current node is on the DFS
 * recursion stack (cycle detection). ArrayDeque.contains() = O(N) linear scan.
 * This code lives in java.base — present in every JDK/JRE.
 *
 * Fix: maintain a HashSet<Node> onStack alongside the Deque.
 * HashSet.contains() = O(1).
 *
 * Exact comparison counts for a linear chain of V nodes (N0→N1→...→N(V-1)):
 *   defective: V*(V-1)/2   (visit(N_k) scans k-element stack = k comparisons;
 *                           sum(k, k=0..V-1) = V*(V-1)/2)
 *   fixed:     V           (1 per visit — one HashSet.contains() call)
 *
 * Derivation of defective count:
 *   visit(N0): stack=[], deque.contains(N0) scans 0 elements → 0 comparisons
 *   visit(N1): stack=[N0], contains(N1) scans 1 element → 1 comparison
 *   visit(N2): stack=[N1,N0], contains(N2) scans 2 elements → 2 comparisons
 *   ...
 *   visit(N(V-1)): stack is V-1 deep → V-1 comparisons
 *   Total: 0+1+2+...+(V-1) = V*(V-1)/2.
 *
 * Growth when V doubles: defective ≈4x (quadratic), fixed ≈2x (linear).
 */
public class TopoSorterAlgorithm {

    public static class Node {
        public final String label;
        public final List<Node> deps = new ArrayList<>();
        public Node(String label) { this.label = label; }
        public void addDep(Node dep) { deps.add(dep); }
        @Override public String toString() { return label; }
    }

    public static class Result {
        public final List<Node> sorted;
        public final long comparisons;
        Result(List<Node> sorted, long comparisons) {
            this.sorted = sorted;
            this.comparisons = comparisons;
        }
    }

    // ─── DEFECTIVE: Deque.contains() for on-stack check ─────────────────────
    // Mirrors ModuleHashesBuilder$TopoSorter.visit() — uses Deque.contains(m)
    // to check whether the current node is already on the recursion stack.

    public static Result topoSortDefective(List<Node> nodes) {
        return new DefectiveSorter().sort(nodes);
    }

    private static class DefectiveSorter {
        private final Deque<Node> stack   = new ArrayDeque<>();
        private final Set<Node>   visited = new HashSet<>();
        private final List<Node>  sorted  = new ArrayList<>();
        private long comparisons = 0;

        Result sort(List<Node> nodes) {
            for (Node n : nodes) {
                if (!visited.contains(n)) visit(n);
            }
            return new Result(sorted, comparisons);
        }

        void visit(Node v) {
            // DEFECT: O(N) scan of the recursion stack for cycle detection
            comparisons += dequeContains(stack, v);
            visited.add(v);
            stack.push(v);
            for (Node dep : v.deps) {
                if (!visited.contains(dep)) visit(dep);
            }
            stack.pop();
            sorted.add(0, v);
        }

        private static long dequeContains(Deque<Node> deque, Node target) {
            long count = 0;
            for (Node n : deque) {
                count++;
                if (n == target) break;
            }
            return count;
        }
    }

    // ─── FIXED: HashSet<Node> for on-stack check ─────────────────────────────
    // Maintain a dedicated onStack set. HashSet.contains() = O(1).

    public static Result topoSortFixed(List<Node> nodes) {
        return new FixedSorter().sort(nodes);
    }

    private static class FixedSorter {
        private final Set<Node>  onStack = new HashSet<>();
        private final Set<Node>  visited = new HashSet<>();
        private final List<Node> sorted  = new ArrayList<>();
        private long comparisons = 0;

        Result sort(List<Node> nodes) {
            for (Node n : nodes) {
                if (!visited.contains(n)) visit(n);
            }
            return new Result(sorted, comparisons);
        }

        void visit(Node v) {
            comparisons++;      // O(1) HashSet.contains() for cycle check
            // onStack.contains(v) would be false here (not a cycle); add anyway
            visited.add(v);
            onStack.add(v);
            for (Node dep : v.deps) {
                if (!visited.contains(dep)) visit(dep);
            }
            onStack.remove(v);
            sorted.add(0, v);
        }
    }

    // ─── Factory ─────────────────────────────────────────────────────────────

    /**
     * Linear chain: N0→N1→...→N(V-1). No cycles — a valid DAG for topo sort.
     * DFS visits nodes in stack-depth order, producing an increasing stack depth
     * at each level.
     *
     * Defective comparisons: V*(V-1)/2
     * Fixed comparisons:     V
     */
    public static List<Node> buildLinearChain(int v) {
        List<Node> nodes = new ArrayList<>();
        for (int i = 0; i < v; i++) nodes.add(new Node("N" + i));
        for (int i = 0; i < v - 1; i++) nodes.get(i).addDep(nodes.get(i + 1));
        return nodes;
    }
}