Design browser history across tabs

Browser History Manager

Design a system to track browser history for multiple tabs. Each tab acts as an independent stack of visited URLs. You need to support navigation, jumping back and forth in time, and visiting new pages.

Requirements

Implement a class BrowserSession with the following methods:

1. visit(tab_id: int, url: str): The user visits a new URL. This clears all 'forward' history for the current tab.
2. back(tab_id: int) -> str: Moves the user back to the previous URL in the tab. Returns the new current URL, or the current URL if no history exists.
3. forward(tab_id: int) -> str: Moves the user forward to the next URL (if available after a 'back' operation). Returns the new current URL.

Constraints

• tab_id is an integer.
• Total number of unique URLs across all tabs is at most 10^5.
• back and forward operations should run in O(1) time.
• visit should run in O(1) time (amortized).

Examples

# Initial state
session = BrowserSession()
session.visit(1, "google.com")
session.visit(1, "github.com")
session.back(1)    # Returns "google.com"
session.forward(1) # Returns "github.com"
session.visit(1, "stackoverflow.com")
session.forward(1) # Returns "stackoverflow.com" (nothing forward)

Edge Cases

• Calling back when on the first page.
• Calling forward after a new visit.
• Handling multiple tab_ids that maintain separate histories.