I was learning about maximum matching in bipartite graphs but I can't understand one thing i.e. **augmenting path always has one extra matching edge.**

Link: Hopcroft Karp Algorithm Geeks for Geeks

**Can someone please help me with this**

Thank you in advance.

Augmenting path has an odd number of edges, let us name them $$$e_0, e_1, e_2, \ldots, e_{2 k}$$$.

The edges selected previously are $$$e_1, e_3, e_5, \ldots, e_{2 k - 1}$$$, there are $$$k$$$ of them.

If we instead select $$$e_0, e_2, e_4, \ldots, e_{2 k}$$$, there are $$$k + 1$$$ of them.

Thank you very much :)