tester's solution of KMHAMHA.

Hello everyone. I was going through the solution of the tester of the problem of kamehameha.
I understood the hashing part but the part i could not understood is the augment function. I mean yeah i have a rough idea what it does but i could not figure out the how that function is able to take care of the various constraints imposed in the original algo of Hopcroft–Karp algorithm( if at all this is the algo implemented here and if not please can you tell me which algo is this). Also i was wondering about the complexity of the solution. At first look it seems like O(VE) solution but the original algo is 0(sqrt(V)*E). Solution can be found here.
Any help would be appreciated. Thanks