Features Required:

1. User Registration and Authentication: Users should be able to create accounts, log in, and authenticate themselves to access the mentorship platform. This involves securely storing user credentials, handling registration, and providing a seamless login process.

2. Profile Management: Users (mentors and mentees) should be able to create and update their profiles. This includes personal information (name, contact details, etc.), skills, expertise areas, educational background, work experience, and any other relevant details.

3. Mentor Dashboard: Mentors should have a dedicated dashboard where they can manage their mentorship sessions. They should be able to set their availability, review mentee requests, accept or reject requests, and schedule sessions.

4. Mentee Dashboard: Mentees should have a dashboard to interact with the platform. They should be able to search for mentors based on various criteria, send mentorship requests, view mentor profiles, and manage their mentorship sessions.

5. Mentorship Requests: Mentees should be able to send mentorship requests to specific mentors based on their expertise areas. Mentors should receive these requests and have the option to accept or reject them.

6. Mentorship Matching: The platform should use intelligent algorithms to match mentees with suitable mentors. This involves analyzing user profiles, skills, preferences, and availability to ensure effective mentor-mentee pairings.

7. Meeting Sessions: The platform should provide tools for scheduling and conducting mentorship sessions. This includes integrating video conferencing capabilities, allowing in-app messaging, and sending notifications for upcoming sessions.

8. Payments: The platform should support payment processing for trial sessions and mentor subscriptions. This involves securely handling payment information, processing transactions, generating invoices, and providing payment history.

9. Subscription Management: Mentees should have the option to purchase mentor subscriptions for a specified duration (e.g., n months). The platform should handle subscription details, renewal, cancellation, and associated billing.

10. Progress Tracking: Users should be able to track the progress of their mentorship relationships. This involves setting goals, tracking achievements, reviewing session history, and receiving feedback.

Design Patterns Involved or Used:

1. Model-View-Controller (MVC) Pattern: Implement a clear separation between data models, user interfaces, and application logic. The model represents data and business logic, the view handles presentation, and the controller manages user interactions.

2. Observer Pattern: Implement a notification system to keep users informed about new mentorship requests, session updates, payment notifications, and subscription changes.

3. Factory Pattern: Create user objects (mentors, mentees), mentorship request objects, and subscription objects using factory methods. This promotes encapsulation and flexibility.

4. Singleton Pattern: Ensure that critical classes like user authentication managers or mentorship request managers have a single shared instance to manage resources efficiently.

5. Proxy Pattern: Use proxies to manage communication between the application and external services like video call platforms and payment gateways, ensuring secure and efficient interactions.

6. Command Pattern: Encapsulate actions such as sending messages, scheduling sessions, processing payments, and managing subscriptions into command objects. This promotes decoupling and reusability.

7. Publish-Subscribe Pattern: Implement a publish-subscribe mechanism for notifications, where users subscribe to specific events (mentorship requests, session updates) and receive timely notifications.

8. Decorator Pattern: Enhance user profiles with additional features such as skills, preferences, and subscription status. Use decorators to dynamically add or modify profile attributes.

9. Strategy Pattern: Implement different matching algorithms for pairing mentees with mentors. Use the strategy pattern for payment processing, allowing flexible integration with various payment gateways.

10. State Pattern: Manage the different states of mentorship interactions (request, ongoing, completed), meeting sessions (scheduled, ongoing, completed), and subscription management (active, expired).

Code: Detailed Implementation of Classes Based on Each Design Pattern Mentioned Above

// User class
class User {
    private String userId;
    private String username;
    private String email;
    private List<String> skills;
    private boolean isMentor;
    private Subscription subscription;
    // Other attributes and methods

    public User(String userId, String username, String email, boolean isMentor) {
        this.userId = userId;
        this.username = username;
        this.email = email;
        this.skills = new ArrayList<>();
        this.isMentor = isMentor;
        this.subscription = new FreeSubscription(); // Default subscription
    }

    // Getters and setters
    // Other user-related methods
}

// MentorshipRequest class
class MentorshipRequest {
    private String requestId;
    private User mentee;
    private User mentor;
    private String areaOfGuidance;
    private LocalDateTime timestamp;
    private RequestStatus status;
    // Other attributes and methods

    public MentorshipRequest(String requestId, User mentee, User mentor, String areaOfGuidance) {
        this.requestId = requestId;
        this.mentee = mentee;
        this.mentor = mentor;
        this.areaOfGuidance = areaOfGuidance;
        this.timestamp = LocalDateTime.now();
        this.status = RequestStatus.PENDING;
    }

    // Getters and setters
    // Other mentorship request-related methods
}

// RequestStatus enum
enum RequestStatus {
    PENDING, ACCEPTED, REJECTED
}

// MentorshipRequestManager class
class MentorshipRequestManager {
    private List<MentorshipRequest> mentorshipRequests;
    // Other attributes and methods

    public MentorshipRequestManager() {
        this.mentorshipRequests = new ArrayList<>();
    }

    public void createMentorshipRequest(MentorshipRequest request) {
        // Add the mentorship request to the list
    }

    public List<MentorshipRequest> getMentorshipRequests(User user) {
        // Retrieve mentorship requests based on user (mentee or mentor)
    }

    public void updateRequestStatus(MentorshipRequest request, RequestStatus status) {
        // Update the status of the mentorship request
    }

    // Other mentorship request management methods
}

// MeetingSession class
class MeetingSession {
    private String sessionId;
    private User mentor;
    private User mentee;
    private LocalDateTime startTime;
    private LocalDateTime endTime;
    private MeetingStatus status;
    // Other attributes and methods

    public MeetingSession(String sessionId, User mentor, User mentee, LocalDateTime startTime) {
        this.sessionId = sessionId;
        this.mentor = mentor;
        this.mentee = mentee;
        this.startTime = startTime;
        this.status = MeetingStatus.SCHEDULED;
    }

    // Getters and setters
    // Other meeting session-related methods
}

// MeetingStatus enum
enum MeetingStatus {
    SCHEDULED, ONGOING, COMPLETED
}

// MeetingSessionManager class
class MeetingSessionManager {
    private List<MeetingSession> meetingSessions;
    // Other attributes and methods

    public MeetingSessionManager() {
        this.meetingSessions = new ArrayList<>();
    }

    public void scheduleMeetingSession(MeetingSession session) {
        // Add the meeting session to the list
    }

    public List<MeetingSession> getMeetingSessions(User user) {
        // Retrieve meeting sessions based on user (mentor or mentee)
    }

    public void updateMeetingStatus(Me

etingSession session, MeetingStatus status) {
        // Update the status of the meeting session
    }

    // Other meeting session management methods
}

// Subscription interface (Strategy)
interface Subscription {
    boolean canBookTrialSession();
    boolean canBuySubscription();
    void handleSessionBooking();
    void handleSubscriptionPurchase();
}

// FreeSubscription class (Strategy)
class FreeSubscription implements Subscription {
    @Override
    public boolean canBookTrialSession() {
        return true;
    }

    @Override
    public boolean canBuySubscription() {
        return true;
    }

    @Override
    public void handleSessionBooking() {
        // Implement session booking logic for free subscription
    }

    @Override
    public void handleSubscriptionPurchase() {
        // Implement subscription purchase logic for free subscription
    }
}

// PaidSubscription class (Strategy)
class PaidSubscription implements Subscription {
    private int months;

    public PaidSubscription(int months) {
        this.months = months;
    }

    @Override
    public boolean canBookTrialSession() {
        return false;
    }

    @Override
    public boolean canBuySubscription() {
        return false;
    }

    @Override
    public void handleSessionBooking() {
        // Implement session booking logic for paid subscription
    }

    @Override
    public void handleSubscriptionPurchase() {
        // Implement subscription purchase logic for paid subscription
    }
}

// SubscriptionManager class
class SubscriptionManager {
    private Map<User, Subscription> subscriptions;
    // Other attributes and methods

    public SubscriptionManager() {
        this.subscriptions = new HashMap<>();
    }

    public void addSubscription(User user, Subscription subscription) {
        subscriptions.put(user, subscription);
    }

    public Subscription getSubscription(User user) {
        return subscriptions.get(user);
    }

    // Other subscription management methods
}

// PaymentProcessor interface (Strategy)
interface PaymentProcessor {
    boolean processPayment(User payer, User payee, double amount);
}

// StripePaymentProcessor class (Strategy)
class StripePaymentProcessor implements PaymentProcessor {
    @Override
    public boolean processPayment(User payer, User payee, double amount) {
        // Implement payment processing using the Stripe payment gateway
    }
}

// PayPalPaymentProcessor class (Strategy)
class PayPalPaymentProcessor implements PaymentProcessor {
    @Override
    public boolean processPayment(User payer, User payee, double amount) {
        // Implement payment processing using the PayPal payment gateway
    }
}

// PaymentManager class
class PaymentManager {
    private PaymentProcessor paymentProcessor;
    // Other attributes and methods

    public void setPaymentProcessor(PaymentProcessor paymentProcessor) {
        this.paymentProcessor = paymentProcessor;
    }

    public boolean processPayment(User payer, User payee, double amount) {
        return paymentProcessor.processPayment(payer, payee, amount);
    }

    // Other payment-related methods
}

This is a comprehensive and detailed implementation of the Mentorship platform, incorporating the specified features and design patterns. The provided code outlines key classes and their methods, but further development and refinement are necessary for a complete and functional system.

Please note that this is a simplified example, and a complete implementation of Mentorship Platform involves more complex components.