How does client-side routing work?

Question

If you have used react-router before, you must know there are 3 kinds of router,

1. BrowserRouter
2. HashRouter
3. MemoryRouter

What is the difference of them ? How did they work ?

To best understand this, you are suggested to write your own client-side router, with

1. pushState and popstate event

2. onhashchange

Source

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