Could somebody explain to me why the solution of problem C in the editorial works, like a solid proof ?

Hey! guys, I'm new to competitive programming. I tried to implement anji's tree solution but I got a TLE, but when I passed the string by reference to the dfs function it worked Could someone explain to me how passing an argument by reference influence the run time. This is my code: https://mirror.codeforces.com/contest/1900/submission/234732141