Vue Circular Dependency Detection

This challenge focuses on building a robust system to detect circular dependencies within Vue.js components. Identifying these cycles is crucial for maintaining application stability, preventing memory leaks, and improving the overall predictability of component interactions and lifecycle hooks.

Problem Description

You are tasked with creating a Vue component that can analyze a given dependency graph of Vue components and identify any circular dependencies. The dependency graph represents which components import or use other components.

Key Requirements:

• Input: The system should accept a dependency graph. This graph can be represented as an adjacency list where keys are component names and values are arrays of component names they depend on.
• Detection: Implement an algorithm to detect cycles in this directed graph.
• Output: The system should return a list of all detected circular dependency paths. Each path should be a sequence of component names forming a cycle, starting and ending with the same component.
• Component Structure: For the purpose of this challenge, assume Vue components are represented by simple string identifiers (e.g., "ComponentA", "UserProfile").

Expected Behavior:

When provided with a dependency graph, the system should accurately identify all cycles. For instance, if "ComponentA" depends on "ComponentB", and "ComponentB" depends on "ComponentA", this should be detected as a cycle: ["ComponentA", "ComponentB", "ComponentA"].

Edge Cases:

• No Dependencies: A component with no dependencies should not cause issues.
• Self-Dependency: A component depending on itself (e.g., "ComponentA" depends on "ComponentA") should be detected as a cycle: ["ComponentA", "ComponentA"].
• Multiple Cycles: The system should be able to detect and report all distinct cycles present in the graph.
• Disconnected Components: The graph might contain components with no connections.

Examples

Example 1:

Input: {
  "App.vue": ["Header.vue", "Footer.vue"],
  "Header.vue": ["Logo.vue"],
  "Footer.vue": [],
  "Logo.vue": ["App.vue"]
}

Output: [
  ["App.vue", "Header.vue", "Logo.vue", "App.vue"]
]

Explanation: App.vue -> Header.vue -> Logo.vue -> App.vue forms a cycle.

Example 2:

Input: {
  "PageA.vue": ["ComponentX.vue"],
  "PageB.vue": ["ComponentY.vue"],
  "ComponentX.vue": ["ComponentY.vue"],
  "ComponentY.vue": ["ComponentX.vue"]
}

Output: [
  ["ComponentX.vue", "ComponentY.vue", "ComponentX.vue"]
]

Explanation: ComponentX.vue -> ComponentY.vue -> ComponentX.vue is a cycle. PageA.vue and PageB.vue are part of the dependency chain but not directly in a cycle.

Example 3: (Self-dependency)

Input: {
  "Dashboard.vue": ["Dashboard.vue"]
}

Output: [
  ["Dashboard.vue", "Dashboard.vue"]
]

Explanation: A direct self-dependency is a valid cycle.

Constraints

• The dependency graph will be represented as a JavaScript object where keys are strings (component names) and values are arrays of strings (dependent component names).
• Component names will consist of alphanumeric characters and periods.
• The number of components will not exceed 1000.
• The total number of dependencies (edges) will not exceed 5000.
• The algorithm's time complexity for detecting cycles should be efficient, ideally O(V + E), where V is the number of vertices (components) and E is the number of edges (dependencies).

Notes

This problem can be approached using graph traversal algorithms. Consider how you would keep track of visited nodes during traversal to identify back-edges, which are indicative of cycles. You will need to manage the state of nodes (e.g., unvisited, visiting, visited) to correctly detect cycles. A Depth First Search (DFS) is a common and effective algorithm for this task. Remember to reset traversal states appropriately when exploring different starting points in the graph to find all cycles.