Add documentation for cycle detection in RBAC

[Copilot]

Documents the Detector interface and DefaultDetector implementation from casbin/casbin PRs #1629 and #1632, which provide cycle detection for role inheritance graphs.

Changes

• docs/CycleDetection.mdx: New page explaining cycle detection mechanics, usage patterns, performance characteristics, and custom detector implementation
• docs/RoleManagerApi.mdx: Added cycle detection reference linking to full documentation
• sidebars.js: Integrated cycle detection under RBAC section

Usage

import (
    "github.com/casbin/casbin/v3"
    "github.com/casbin/casbin/v3/detector"
)

e, _ := casbin.NewEnforcer("model.conf", "policy.csv")
d := detector.NewDefaultDetector()

if err := d.Check(e.GetRoleManager()); err != nil {
    // err describes the cycle: "cycle detected: role_a -> role_b -> role_c -> role_a"
    log.Fatal(err)
}

The detector uses DFS to identify cycles in O(n) time where n is the number of roles and relationships.

Warning

Firewall rules blocked me from connecting to one or more addresses (expand for details)

I tried to connect to the following addresses, but was blocked by firewall rules:

• https://api.github.com/repos/casbin/casbin/pulls/1629
  • Triggering command: /usr/bin/curl curl -s REDACTED (http block)

If you need me to access, download, or install something from one of these locations, you can either:

• Configure Actions setup steps to set up my environment, which run before the firewall is enabled
• Add the appropriate URLs or hosts to the custom allowlist in this repository's Copilot coding agent settings (admins only)

Original prompt

---

This section details on the original issue you should resolve

<issue_title>[docs] add docs for the PRs: 1629, 1632</issue_title>
<issue_description>Improve the related docs page based on the newly merged PRs: apache/casbin#1629 and apache/casbin#1632
You should write high-quality human-like docs for a modern OSS software. Don't write in the GPT-flavor. Don't write too long, keep it tidy docs. Don't use itemized list to describe things like "Use Cases", "Best practice" or "what it can do"
don't change yarn.lock
Don't add too long text, keep it short and to the point
Don't add the docs in a template like one section name and one text paragraph. You need to organize the content to be user-friendly and not boring for users to read
</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes [docs] add docs for the PRs: 1629, 1632 #434

---

💬 We'd love your input! Share your thoughts on Copilot coding agent in our 2 minute survey.

[netlify]

✅ Deploy Preview for casbin ready!

Name	Link
🔨 Latest commit	2f384a3
🔍 Latest deploy log	https://app.netlify.com/projects/casbin/deploys/6956a04e6f54530008860446
😎 Deploy Preview	https://deploy-preview-435--casbin.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

---

To edit notification comments on pull requests, go to your Netlify project configuration.

[CLAassistant]

Thank you for your submission! We really appreciate it. Like many open source projects, we ask that you sign our Contributor License Agreement before we can accept your contribution.
_{You have signed the CLA already but the status is still pending? Let us recheck it.}