feat: v5 algorithm detect cycle (#74)

* feat: add direction flag and visitOnce flag to dfs

* feat: v5 algorithm detect cycle

* test: unit test of detect cycle algorithm

Author: zqqcee

__tests__/data/detect-cycle-test-data.json

@@ -87,10 +87,8 @@ const data = {
 const graph = new Graph<any, any>(data);
 describe('depthFirstSearch', () => {
   it('should perform DFS operation on graph', () => {
-
     const enterNodeCallback = jest.fn();
     const leaveNodeCallback = jest.fn();
-
     // Traverse graphs without callbacks first to check default ones.
     depthFirstSearch(graph, 'A');
 

__tests__/unit/detect-cycle.spec.ts

@@ -9,7 +9,7 @@ export const dataTransformer = (data: { nodes: { id: NodeID, [key: string]: any
     return {
         nodes: nodes.map((n) => {
             const { id, ...rest } = n;
-            return { id, data: rest };
+            return { id, data: rest ? rest : {} };
         }),
         edges: edges.map((e, i) => {
             const { id, source, target, ...rest } = e;

__tests__/unit/dfs.spec.ts

@@ -21,7 +21,7 @@
     "build:ci": "pnpm -r run build:ci",
     "prepare": "husky install",
     "test": "jest",
-    "test_one": "jest ./__tests__/unit/mst.spec.ts",
+    "test_one": "jest ./__tests__/unit/detect-cycle.spec.ts",
     "coverage": "jest --coverage",
     "build:site": "vite build",
     "deploy": "gh-pages -d site/dist",

__tests__/utils/data.ts

@@ -0,0 +1,307 @@
+import { depthFirstSearch } from './dfs';
+import { getConnectedComponents, detectStrongConnectComponents } from './connected-component';
+import { Graph, IAlgorithmCallbacks, INode, NodeData, NodeID } from './types';
+import { Node } from '@antv/graphlib';
+
+/**
+ * Detects a directed cycle in a graph.
+ *
+ * @param graph The graph to detect the directed cycle in.
+ * @returns An object representing the detected directed cycle, where each key-value pair represents a node ID and its parent node ID in the cycle.
+ */
+export const detectDirectedCycle = (graph: Graph): {
+    [key: NodeID]: NodeID;
+} => {
+    let cycle: {
+        [key: NodeID]: NodeID;
+    } = null;
+    const nodes = graph.getAllNodes();
+    const dfsParentMap: { [key: NodeID]: NodeID } = {};
+    // The set of all nodes that are not being accessed
+    const unvisitedSet: { [key: NodeID]: Node<NodeData> } = {};
+    // The set of nodes being accessed
+    const visitingSet: { [key: NodeID]: NodeID } = {};
+    // The set of all nodes that have been accessed
+    const visitedSet: { [key: NodeID]: NodeID } = {};
+    // init unvisitedSet
+    nodes.forEach((node) => {
+        unvisitedSet[node.id] = node;
+    });
+    const callbacks: IAlgorithmCallbacks = {
+        enter: ({ current: currentNodeId, previous: previousNodeId }) => {
+            if (visitingSet[currentNodeId]) {
+                // 如果当前节点正在访问中，则说明检测到环路了
+                cycle = {};
+                let currentCycleNodeId = currentNodeId;
+                let previousCycleNodeId = previousNodeId;
+                while (previousCycleNodeId !== currentNodeId) {
+                    cycle[currentCycleNodeId] = previousCycleNodeId;
+                    currentCycleNodeId = previousCycleNodeId;
+                    previousCycleNodeId = dfsParentMap[previousCycleNodeId];
+                }
+                cycle[currentCycleNodeId] = previousCycleNodeId;
+            } else {
+                visitingSet[currentNodeId] = currentNodeId;
+                delete unvisitedSet[currentNodeId];
+                dfsParentMap[currentNodeId] = previousNodeId;
+            }
+        },
+        leave: ({ current: currentNodeId }) => {
+            visitedSet[currentNodeId] = currentNodeId;
+            delete visitingSet[currentNodeId];
+        },
+        allowTraversal: () => {
+            if (cycle) {
+                return false;
+            }
+            return true;
+        },
+    };
+    for (let key of Object.keys(unvisitedSet)) {
+        depthFirstSearch(graph, key, callbacks, true, false);
+    }
+    return cycle;
+};
+
+/**
+ * Detects all undirected cycles in a graph.
+ * @param graph The graph to detect cycles in.
+ * @param nodeIds Optional array of node IDs to filter cycles by.
+ * @param include Specifies whether the filtered cycles should be included (true) or excluded (false).
+ * @returns An array of objects representing the detected cycles in the graph.
+ */
+export const detectAllUndirectedCycle = (graph: Graph, nodeIds?: NodeID[], include = true) => {
+    const allCycles: { [key: NodeID]: INode }[] = [];
+    const components = getConnectedComponents(graph, false);
+    // loop through all connected components
+    for (const component of components) {
+        if (!component.length) continue;
+        const root = component[0];
+        const rootId = root.id;
+        const stack = [root];
+        const parent = { [rootId]: root };
+        const used = { [rootId]: new Set() };
+        // walk a spanning tree to find cycles
+        while (stack.length > 0) {
+            const curNode = stack.pop();
+            const curNodeId = curNode.id;
+            const neighbors = graph.getNeighbors(curNodeId);
+            // const neighbors = getNeighbors(curNodeId, graphData.edges);
+            for (let i = 0; i < neighbors.length; i += 1) {
+                const neighborId = neighbors[i].id;
+                const neighbor = graph.getAllNodes().find(node => node.id === neighborId);
+                if (neighborId === curNodeId) {
+                    allCycles.push({ [neighborId]: curNode });
+                } else if (!(neighborId in used)) {
+                    // visit a new node
+                    parent[neighborId] = curNode;
+                    stack.push(neighbor);
+                    used[neighborId] = new Set([curNode]);
+                } else if (!used[curNodeId].has(neighbor)) {
+                    // a cycle found
+                    let cycleValid = true;
+                    const cyclePath = [neighbor, curNode];
+                    let p = parent[curNodeId];
+                    while (used[neighborId].size && !used[neighborId].has(p)) {
+                        cyclePath.push(p);
+                        if (p === parent[p.id]) break;
+                        else p = parent[p.id];
+                    }
+                    cyclePath.push(p);
+                    if (nodeIds && include) {
+                        cycleValid = false;
+                        if (cyclePath.findIndex((node) => nodeIds.indexOf(node.id) > -1) > -1) {
+                            cycleValid = true;
+                        }
+                    } else if (nodeIds && !include) {
+                        if (cyclePath.findIndex((node) => nodeIds.indexOf(node.id) > -1) > -1) {
+                            cycleValid = false;
+                        }
+                    }
+                    // Format node list to cycle 
+                    if (cycleValid) {
+                        const cycle: { [key: NodeID]: INode } = {};
+                        for (let index = 1; index < cyclePath.length; index += 1) {
+                            cycle[cyclePath[index - 1].id] = cyclePath[index];
+                        }
+                        if (cyclePath.length) {
+                            cycle[cyclePath[cyclePath.length - 1].id] = cyclePath[0];
+                        }
+                        allCycles.push(cycle);
+                    }
+                    used[neighborId].add(curNode);
+                }
+            }
+        }
+    }
+    return allCycles;
+};
+
+/**
+ * Detects all directed cycles in a graph.
+ * @param graph The graph to detect cycles in.
+ * @param nodeIds Optional array of node IDs to filter cycles by.
+ * @param include Specifies whether the filtered cycles should be included (true) or excluded (false).
+ * @returns An array of objects representing the detected cycles in the graph.
+ */
+export const detectAllDirectedCycle = (graph: Graph, nodeIds?: NodeID[], include = true) => {
+    const path: INode[] = []; // stack of nodes in current pate
+    const blocked = new Set<INode>();
+    const B: { [key: NodeID]: Set<INode> } = {}; // remember portions of the graph that yield no elementary circuit
+    const allCycles: { [key: NodeID]: INode }[] = [];
+    const idx2Node: {
+        [key: number]: INode;
+    } = {};
+    const node2Idx: { [key: NodeID]: number } = {};
+    // unblock all blocked nodes
+    const unblock = (thisNode: INode) => {
+        const stack = [thisNode];
+        while (stack.length > 0) {
+            const node = stack.pop();
+            if (blocked.has(node)) {
+                blocked.delete(node);
+                B[node.id].forEach((n) => {
+                    stack.push(n);
+                });
+                B[node.id].clear();
+            }
+        }
+    };
+
+    const circuit = (node: INode, start: INode, adjList: { [key: NodeID]: number[] }) => {
+        let closed = false; // whether a path is closed
+        if (nodeIds && include === false && nodeIds.indexOf(node.id) > -1) return closed;
+        path.push(node);
+        blocked.add(node);
+        const neighbors = adjList[node.id];
+        for (let i = 0; i < neighbors.length; i += 1) {
+            const neighbor = idx2Node[neighbors[i]];
+            if (neighbor === start) {
+                const cycle: { [key: NodeID]: INode } = {};
+                for (let index = 1; index < path.length; index += 1) {
+                    cycle[path[index - 1].id] = path[index];
+                }
+                if (path.length) {
+                    cycle[path[path.length - 1].id] = path[0];
+                }
+                allCycles.push(cycle);
+                closed = true;
+            } else if (!blocked.has(neighbor)) {
+                if (circuit(neighbor, start, adjList)) {
+                    closed = true;
+                }
+            }
+        }
+        if (closed) {
+            unblock(node);
+        } else {
+            for (let i = 0; i < neighbors.length; i += 1) {
+                const neighbor = idx2Node[neighbors[i]];
+                if (!B[neighbor.id].has(node)) {
+                    B[neighbor.id].add(node);
+                }
+            }
+        }
+        path.pop();
+        return closed;
+    };
+
+    const nodes = graph.getAllNodes();
+
+    // Johnson's algorithm, sort nodes
+    for (let i = 0; i < nodes.length; i += 1) {
+        const node = nodes[i];
+        const nodeId = node.id;
+        node2Idx[nodeId] = i;
+        idx2Node[i] = node;
+    }
+    // If there are specified included nodes, the specified nodes are sorted first in order to end the search early
+    if (nodeIds && include) {
+        for (let i = 0; i < nodeIds.length; i++) {
+            const nodeId = nodeIds[i];
+            node2Idx[nodes[i].id] = node2Idx[nodeId];
+            node2Idx[nodeId] = 0;
+            idx2Node[0] = nodes.find(node => node.id === nodeId);
+            idx2Node[node2Idx[nodes[i].id]] = nodes[i];
+        }
+    }
+
+    // Returns the adjList of the strongly connected component of the node (order > = nodeOrder)
+    const getMinComponentAdj = (components: INode[][]) => {
+        let minCompIdx;
+        let minIdx = Infinity;
+        // Find least component and the lowest node
+        for (let i = 0; i < components.length; i += 1) {
+            const comp = components[i];
+            for (let j = 0; j < comp.length; j++) {
+                const nodeIdx = node2Idx[comp[j].id];
+                if (nodeIdx < minIdx) {
+                    minIdx = nodeIdx;
+                    minCompIdx = i;
+                }
+            }
+        }
+        const component = components[minCompIdx];
+        const adjList: { [key: NodeID]: number[] } = {};
+        for (let i = 0; i < component.length; i += 1) {
+            const node = component[i];
+            adjList[node.id] = [];
+            for (const neighbor of graph.getRelatedEdges(node.id, "out").map(n => n.target).filter((n) => component.map(c => c.id).indexOf(n) > -1)) {
+                // 对自环情况 (点连向自身) 特殊处理：记录自环，但不加入adjList
+                if (neighbor === node.id && !(include === false && nodeIds.indexOf(node.id) > -1)) {
+                    allCycles.push({ [node.id]: node });
+                } else {
+                    adjList[node.id].push(node2Idx[neighbor]);
+                }
+            }
+        }
+        return {
+            component,
+            adjList,
+            minIdx,
+        };
+    };
+
+    let nodeIdx = 0;
+    while (nodeIdx < nodes.length) {
+        const sccs = detectStrongConnectComponents(graph).filter(
+            (component) => component.length > 1,
+        );
+        if (sccs.length === 0) break;
+        const scc = getMinComponentAdj(sccs);
+        const { minIdx, adjList, component } = scc;
+        if (component.length > 1) {
+            component.forEach((node) => {
+                B[node.id] = new Set();
+            });
+            const startNode = idx2Node[minIdx];
+            // StartNode is not in the specified node to include. End the search ahead of time.
+            if (nodeIds && include && nodeIds.indexOf(startNode.id) === -1) return allCycles;
+            circuit(startNode, startNode, adjList);
+            nodeIdx = minIdx + 1;
+        } else {
+            break;
+        }
+        break;
+    }
+    return allCycles;
+};
+
+/**
+ * Detects all cycles in a graph.
+ * @param graph The graph to detect cycles in.
+ * @param directed Specifies whether the graph is directed (true) or undirected (false).
+ * @param nodeIds Optional array of node IDs to filter cycles by.
+ * @param include Specifies whether the filtered cycles should be included (true) or excluded (false).
+ * @returns An array of objects representing the detected cycles in the graph.
+ */
+export const detectAllCycles = (
+    graph: Graph,
+    directed?: boolean,
+    nodeIds?: string[],
+    include = true,
+) => {
+    if (directed) return detectAllDirectedCycle(graph, nodeIds, include);
+    return detectAllUndirectedCycle(graph, nodeIds, include);
+};
+