java-topology/defects/nim/unit/NimCyclicTreeAlgorithm.java

package unit;

import java.util.*;

/**
 * NimCyclicTreeAlgorithm — CWE-407 test for nim-0002
 *
 * Models trees.cyclicTreeAux(n, visited):
 *   slow: for v in visited: if v == n — O(N) scan per node, O(N²) for path tree
 *   fast: HashSet[pointer] visited — O(1) per node, O(N) total
 *
 * Test: on a path graph (depth=N), slow does O(N²) scans; fast does O(N) ops.
 */
public class NimCyclicTreeAlgorithm {

    // Simple tree node (PNode proxy)
    static class PNode {
        final int id;
        final List<PNode> sons;
        PNode(int id) { this.id = id; this.sons = new ArrayList<>(); }
    }

    // --- SLOW: O(N²) ---
    // for v in visited: if v == n: return true
    // visited is a path-stack (ArrayList acting as seq with add/remove)
    static class SlowCyclicCheck {
        long scanOps = 0;

        boolean cyclicTreeAux(PNode n, List<PNode> visited) {
            if (n == null) return false;
            // Linear scan of visited (the path stack)
            for (PNode v : visited) {
                scanOps++;
                if (v == n) return true;
            }
            visited.add(n);
            for (PNode son : n.sons) {
                if (cyclicTreeAux(son, visited)) return true;
            }
            visited.remove(visited.size() - 1);
            return false;
        }

        boolean cyclicTree(PNode n) {
            List<PNode> visited = new ArrayList<>();
            return cyclicTreeAux(n, visited);
        }
    }

    // --- FAST: O(N) ---
    // visited is a HashSet[pointer] (IdentityHashMap backed set)
    static class FastCyclicCheck {
        long hashOps = 0;

        // Using IdentityHashMap to simulate pointer-based HashSet
        boolean cyclicTreeAux(PNode n, Set<PNode> visited) {
            if (n == null) return false;
            hashOps++;
            if (visited.contains(n)) return true;  // O(1) identity hash
            visited.add(n);
            for (PNode son : n.sons) {
                if (cyclicTreeAux(son, visited)) return true;
            }
            visited.remove(n);
            return false;
        }

        boolean cyclicTree(PNode n) {
            // IdentityHashMap simulates pointer-equality HashSet (Nim's HashSet[pointer])
            Set<PNode> visited = Collections.newSetFromMap(new IdentityHashMap<>());
            return cyclicTreeAux(n, visited);
        }
    }

    // Build an acyclic path graph: 0 -> 1 -> 2 -> ... -> n-1
    // This is worst case for the slow algorithm: depth = n, visited grows to n
    static PNode buildPathGraph(int n) {
        PNode[] nodes = new PNode[n];
        for (int i = 0; i < n; i++) nodes[i] = new PNode(i);
        for (int i = 0; i < n - 1; i++) nodes[i].sons.add(nodes[i + 1]);
        return nodes[0];
    }

    // Build a balanced binary tree of depth d (no cycles)
    static PNode buildBinaryTree(int depth) {
        if (depth == 0) return new PNode(0);
        PNode root = new PNode(depth);
        root.sons.add(buildBinaryTree(depth - 1));
        root.sons.add(buildBinaryTree(depth - 1));
        return root;
    }

    public static void main(String[] args) {
        System.out.println("NimCyclicTreeAlgorithm — nim-0002");
        System.out.println("  Pattern: for v in visited: if v == n — O(N²) vs HashSet — O(N)");
        System.out.println();

        int passed = 0;
        int total = 0;

        // Test 1: Path graphs (worst case for O(N²))
        int[] pathSizes = {100, 300, 500, 800};
        for (int n : pathSizes) {
            PNode root = buildPathGraph(n);

            SlowCyclicCheck slow = new SlowCyclicCheck();
            FastCyclicCheck fast = new FastCyclicCheck();

            boolean slowResult = slow.cyclicTree(root);
            boolean fastResult = fast.cyclicTree(root);

            long slowOps = slow.scanOps;
            long fastOps = fast.hashOps;

            // No cycles — both should return false
            boolean correctResult = !slowResult && !fastResult;

            // Slow: at depth d, visited has d nodes. Sum for path of N nodes: 0+1+2+...+(N-1) = N(N-1)/2
            boolean slowIsQuadratic = slowOps >= (long) n * (n - 1) / 4; // conservative
            boolean fastIsLinear = fastOps <= n + 1; // at most N+1 hash checks

            total += 3;
            if (correctResult) { System.out.println("PASS path N=" + n + ": no cycle detected (correct)"); passed++; }
            else { System.out.println("FAIL path N=" + n + ": wrong cycle detection slow=" + slowResult + " fast=" + fastResult); }

            if (slowIsQuadratic) { System.out.println("PASS path N=" + n + ": slow O(N²) scans=" + slowOps + " >= N(N-1)/4=" + (n * (n - 1) / 4)); passed++; }
            else { System.out.println("FAIL path N=" + n + ": slow not quadratic, scans=" + slowOps); }

            if (fastIsLinear) { System.out.println("PASS path N=" + n + ": fast O(N) ops=" + fastOps + " <= N+1=" + (n + 1)); passed++; }
            else { System.out.println("FAIL path N=" + n + ": fast not linear, ops=" + fastOps); }
        }

        // Test 2: Cycle detection correctness — introduce a back edge
        {
            PNode[] nodes = new PNode[5];
            for (int i = 0; i < 5; i++) nodes[i] = new PNode(i);
            nodes[0].sons.add(nodes[1]);
            nodes[1].sons.add(nodes[2]);
            nodes[2].sons.add(nodes[0]); // cycle: 2 -> 0

            SlowCyclicCheck slow = new SlowCyclicCheck();
            FastCyclicCheck fast = new FastCyclicCheck();

            boolean slowDetects = slow.cyclicTree(nodes[0]);
            boolean fastDetects = fast.cyclicTree(nodes[0]);

            total += 2;
            if (slowDetects) { System.out.println("PASS cycle: slow correctly detects cycle"); passed++; }
            else { System.out.println("FAIL cycle: slow missed cycle"); }
            if (fastDetects) { System.out.println("PASS cycle: fast correctly detects cycle"); passed++; }
            else { System.out.println("FAIL cycle: fast missed cycle"); }
        }

        System.out.println();
        System.out.println(passed + "/" + total + " PASS");
        if (passed != total) {
            throw new AssertionError(passed + "/" + total + " tests passed");
        }
    }
}