feat(core): Handle cycles in workflows when partially executing them

packages/core/src/PartialExecutionUtils/DirectedGraph.ts

@@ -286,6 +286,149 @@ export class DirectedGraph {
 		);
 	}
 
+	/**
+	 * Returns all strongly connected components.
+	 *
+	 * Strongly connected components are a set of nodes where it's possible to
+	 * reach every node from every node.
+	 *
+	 * Strongly connected components are mutually exclusive in directed graphs,
+	 * e.g. they cannot overlap.
+	 *
+	 * The smallest strongly connected component is a single node, since it can
+	 * reach itself from itself by not following any edges.
+	 *
+	 * The algorithm implement here is Tarjan's algorithm.
+	 *
+	 * Example:
+	 * ┌─────┐    ┌─────┐    ┌─────┐    ┌─────┐
+	 * │node1├────►node2◄────┤node3├────►node5│
+	 * └─────┘    └──┬──┘    └──▲──┘    └▲───┬┘
+	 *               │          │        │   │
+	 *            ┌──▼──┐       │       ┌┴───▼┐
+	 *            │node4├───────┘       │node6│
+	 *            └─────┘               └─────┘
+	 *
+	 * The strongly connected components are
+	 * 1. node1
+	 * 2. node2, node4, node3
+	 * 3. node5, node6
+	 *
+	 * Further reading:
+	 * https://en.wikipedia.org/wiki/Strongly_connected_component
+	 * https://www.youtube.com/watch?v=wUgWX0nc4NY
+	 */
+	getStronglyConnectedComponents(): INode[][] {
+		let id = 0;
+		const visited: Set<INode> = new Set();
+		const ids: Map<INode, number> = new Map();
+		const lows: Map<INode, number> = new Map();
+		const stack: INode[] = [];
+		const stronglyConnectedComponents: INode[][] = [];
+
+		const followNode = (node: INode) => {
+			if (visited.has(node)) {
+				return;
+			}
+
+			visited.add(node);
+			lows.set(node, id);
+			ids.set(node, id);
+			id++;
+			stack.push(node);
+
+			const directChildren = this.getDirectChildConnections(node).map((c) => c.to);
+			for (const child of directChildren) {
+				followNode(child);
+
+				// if node is on stack min the low id
+				if (stack.includes(child)) {
+					const childId = lows.get(child);
+					const ownId = lows.get(node);
+					a.ok(childId !== undefined);
+					a.ok(ownId !== undefined);
+					const lowId = Math.min(childId, ownId);
+
+					lows.set(node, lowId);
+				}
+			}
+
+			// after we visited all children, check if the low id is the same as the
+			// nodes id, which means we found a strongly connected component
+			const ownId = ids.get(node);
+			const ownLow = lows.get(node);
+			a.ok(ownId !== undefined);
+			a.ok(ownLow !== undefined);
+
+			if (ownId === ownLow) {
+				// pop from the stack until the stack is empty or we find a node that
+				// has a different low id
+				const scc: INode[] = [];
+				let next = stack.at(-1);
+
+				while (next && lows.get(next) === ownId) {
+					stack.pop();
+					scc.push(next);
+					next = stack.at(-1);
+				}
+
+				if (scc.length > 0) {
+					stronglyConnectedComponents.push(scc);
+				}
+			}
+		};
+
+		for (const node of this.nodes.values()) {
+			followNode(node);
+		}
+
+		return stronglyConnectedComponents;
+	}
+
+	private depthFirstSearchRecursive(
+		from: INode,
+		fn: (node: INode) => boolean,
+		seen: Set<INode>,
+	): INode | undefined {
+		if (seen.has(from)) {
+			return;
+		}
+		seen.add(from);
+
+		if (fn(from)) {
+			return from;
+		}
+
+		for (const childConnection of this.getDirectChildConnections(from)) {
+			const found = this.depthFirstSearchRecursive(childConnection.to, fn, seen);
+
+			if (found) {
+				return found;
+			}
+		}
+
+		return;
+	}
+
+	/**
+	 * Like `Array.prototype.find` but for directed graphs.
+	 *
+	 * Starting from, and including, the `from` node this calls the provided
+	 * predicate function with every child node until the predicate function
+	 * returns true.
+	 *
+	 * The search is depth first, meaning every branch is exhausted before the
+	 * next branch is tried.
+	 *
+	 * The first node for which the predicate function returns true is returned.
+	 *
+	 * If the graph is exhausted and the predicate function never returned true,
+	 * undefined is returned instead.
+	 */
+	depthFirstSearch({ from, fn }: { from: INode; fn: (node: INode) => boolean }): INode | undefined {
+		return this.depthFirstSearchRecursive(from, fn, new Set());
+	}
+
 	toWorkflow(parameters: Omit<WorkflowParameters, 'nodes' | 'connections'>): Workflow {
 		return new Workflow({
 			...parameters,

packages/core/src/PartialExecutionUtils/__tests__/DirectedGraph.test.ts

@@ -9,6 +9,7 @@
 // XX denotes that the node is disabled
 // PD denotes that the node has pinned data
 
+import type { INode } from 'n8n-workflow';
 import { NodeConnectionType } from 'n8n-workflow';
 
 import { createNodeData, defaultWorkflowParameter } from './helpers';
@@ -89,6 +90,105 @@ describe('DirectedGraph', () => {
 		});
 	});
 
+	describe('getStronglyConnectedComponents', () => {
+		// ┌─────┐    ┌─────┐    ┌─────┐
+		// │node1├───►│node2├───►│node4│
+		// └─────┘    └──┬──┘    └─────┘
+		//    ▲          │
+		//    │          │
+		// ┌──┴──┐       │
+		// │node3│◄──────┘
+		// └─────┘
+		test('find strongly connected components', () => {
+			// ARRANGE
+			const node1 = createNodeData({ name: 'Node1' });
+			const node2 = createNodeData({ name: 'Node2' });
+			const node3 = createNodeData({ name: 'Node3' });
+			const node4 = createNodeData({ name: 'Node4' });
+			const graph = new DirectedGraph()
+				.addNodes(node1, node2, node3, node4)
+				.addConnections(
+					{ from: node1, to: node2 },
+					{ from: node2, to: node3 },
+					{ from: node3, to: node1 },
+					{ from: node2, to: node4 },
+				);
+
+			// ACT
+			const stronglyConnectedComponents = graph.getStronglyConnectedComponents();
+
+			// ASSERT
+			expect(stronglyConnectedComponents).toHaveLength(2);
+			expect(stronglyConnectedComponents).toContainEqual([node4]);
+			expect(stronglyConnectedComponents).toContainEqual([node3, node2, node1]);
+		});
+
+		// TODO: create diagram
+		test('find strongly connected components even if they use different output indexes', () => {
+			// ARRANGE
+			const trigger = createNodeData({ name: 'trigger' });
+			const loop = createNodeData({ name: 'loop' });
+			const node = createNodeData({ name: 'node' });
+			const graph = new DirectedGraph()
+				.addNodes(trigger, loop, node)
+				.addConnections(
+					{ from: trigger, to: loop },
+					{ from: loop, outputIndex: 1, to: node },
+					{ from: node, to: loop },
+				);
+
+			// ACT
+			const stronglyConnectedComponents = graph.getStronglyConnectedComponents();
+
+			// ASSERT
+			expect(stronglyConnectedComponents).toHaveLength(2);
+			expect(stronglyConnectedComponents).toContainEqual([trigger]);
+			expect(stronglyConnectedComponents).toContainEqual([node, loop]);
+		});
+	});
+
+	describe('depthFirstSearch', () => {
+		// ┌─────┐    ┌─────┐    ┌─────┐    ┌─────┐    ┌─────┐
+		// │node0├───►│node1├───►│node2├───►│node4│───►│node5│
+		// └─────┘    └─────┘    └──┬──┘    └─────┘    └─────┘
+		//               ▲          │
+		//               │          │
+		//            ┌──┴──┐       │
+		//            │node3│◄──────┘
+		//            └─────┘
+		test('calls nodes in the correct order and stops when it found the node', () => {
+			// ARRANGE
+			const node0 = createNodeData({ name: 'Node0' });
+			const node1 = createNodeData({ name: 'Node1' });
+			const node2 = createNodeData({ name: 'Node2' });
+			const node3 = createNodeData({ name: 'Node3' });
+			const node4 = createNodeData({ name: 'Node4' });
+			const node5 = createNodeData({ name: 'Node5' });
+			const graph = new DirectedGraph()
+				.addNodes(node0, node1, node2, node3, node4, node5)
+				.addConnections(
+					{ from: node0, to: node1 },
+					{ from: node1, to: node2 },
+					{ from: node2, to: node3 },
+					{ from: node3, to: node1 },
+					{ from: node2, to: node4 },
+					{ from: node4, to: node5 },
+				);
+			const fn = jest.fn().mockImplementation((node: INode) => node === node4);
+
+			// ACT
+			const foundNode = graph.depthFirstSearch({
+				from: node0,
+				fn,
+			});
+
+			// ASSERT
+			expect(foundNode).toBe(node4);
+			expect(fn).toHaveBeenCalledTimes(5);
+			expect(fn.mock.calls).toEqual([[node0], [node1], [node2], [node3], [node4]]);
+		});
+	});
+
 	describe('getParentConnections', () => {
 		// ┌─────┐   ┌─────┐   ┌─────┐   ┌─────┐
 		// │node1├──►│node2├──►│node3│──►│node4│

packages/core/src/PartialExecutionUtils/__tests__/cleanRunData.test.ts

@@ -23,7 +23,7 @@ describe('cleanRunData', () => {
 		};
 
 		// ACT
-		const newRunData = cleanRunData(runData, graph, [node1]);
+		const newRunData = cleanRunData(runData, graph, new Set([node1]));
 
 		// ASSERT
 		expect(newRunData).toEqual({});
@@ -47,7 +47,7 @@ describe('cleanRunData', () => {
 		};
 
 		// ACT
-		const newRunData = cleanRunData(runData, graph, [node2]);
+		const newRunData = cleanRunData(runData, graph, new Set([node2]));
 
 		// ASSERT
 		expect(newRunData).toEqual({ [node1.name]: runData[node1.name] });
@@ -78,7 +78,7 @@ describe('cleanRunData', () => {
 		};
 
 		// ACT
-		const newRunData = cleanRunData(runData, graph, [node2]);
+		const newRunData = cleanRunData(runData, graph, new Set([node2]));
 
 		// ASSERT
 		// TODO: Find out if this is a desirable result in milestone 2