Design Browser History

A browser tab starts on a homepage. From the page it is on, it can visit a new page, go back a number of pages in its history, or go forward again. Visiting a new page erases the pages you could have gone forward to, the way a real browser does.

Implement the class BrowserHistory:

• BrowserHistory(homepage) starts the tab on the page homepage.
• visit(url) goes from the current page to url. Every page ahead of the current page (the pages forward could reach) is erased from the history.
• back(steps) goes back steps pages. If fewer than steps pages are behind the current one, it goes back as far as it can, to the homepage. It returns the url of the page it ends on.
• forward(steps) goes forward steps pages, or as far as it can if fewer pages are ahead. It returns the url of the page it ends on.

The input is the homepage and a list of operations, applied in order to one new BrowserHistory. The output lists what the back and forward calls return, in order. The starter code spells these names the way your language does.

Example 1:

Input:
    BrowserHistory("start.com")
    visit("news.com")
    visit("shop.com")
    visit("video.com")
    back(1)
    back(1)
    forward(1)
    visit("jobs.com")
    forward(2)
    back(2)
    back(7)
Output: shop.com news.com shop.com jobs.com news.com start.com
Explanation:
The history is start.com, news.com, shop.com, video.com, and the tab is on video.com.
back(1) goes to shop.com, the next back(1) to news.com, and forward(1) to shop.com again.
visit("jobs.com") erases video.com, the page that was ahead:
the history is now start.com, news.com, shop.com, jobs.com.
forward(2) can't move, because no page is ahead: it stays on jobs.com.
back(2) goes to news.com. back(7) can only go back one more page, to start.com.

Example 2:

Input:
    BrowserHistory("home.com")
    back(1)
    visit("a.com")
    visit("b.com")
    back(5)
    forward(1)
    forward(9)
Output: home.com home.com a.com b.com
Explanation: Nothing is behind the homepage, so back(1) stays on home.com. From b.com only two pages are behind,
so back(5) goes back two pages, to home.com. forward(9) goes forward as far as it can, to b.com.

Example 3:

Input:
    BrowserHistory("home.com")
    visit("a.com")
    visit("b.com")
    visit("c.com")
    back(2)
    visit("d.com")
    forward(1)
    back(1)
    forward(2)
Output: a.com d.com a.com d.com
Explanation: After back(2) the tab is on a.com, with b.com and c.com ahead. visit("d.com") erases both:
the history is now home.com, a.com, d.com. So forward(1) stays on d.com, and from a.com forward(2) can only reach d.com.

Constraints:

• 1 <= homepage.length, url.length <= 20
• homepage and url consist of lowercase English letters and '.'.
• 1 <= steps <= 105
• At most 105 calls in total are made to visit, back and forward.