推式-PKUWC2018 随机游走

\[f_u=p_uf_{a_u}+q_u\\ \begin{aligned} f_u=&\frac{1}{d_u}\left(f_{a_u}+\sum_{u\to v}f_v\right)+1\\ =&\frac{1}{d_u}\left(f_{a_u}+\sum_{u\to v}(p_vf_u+q_v)\right)+1\\ =&\frac{1}{d_u}\left(f_{a_u}+sp_uf_u+sq_u\right)+1\\ \end{aligned}\\ \left(1-\frac{1}{d_u}sp_u\right)f_u=\frac{1}{d_u}\left(f_{a_u}+sq_u\right)+1\\ (d_u-sp_u)f_u=f_{a_u}+sq_u+d_u\\ f_u=\frac{f_{a_u}}{d_u-sp_u}+\frac{sq_u+d_u}{d_u-sp_u}\\ p_u=\frac{1}{d_u-sp_u}\\ q_u=\frac{sq_u+d_u}{d_u-sp_u}\\ (\forall u\in S,p_u=q_u=0) \]