Algorithm 1:Exact Greedy Algorithm for Split Finding.

Input:$I$, instance set of the current node

Input:$d$, feature dimension

$gain\leftarrow 0$

$G\leftarrow {\displaystyle \sum }_{i\in I}{g}_i,H\leftarrow {\displaystyle \sum }_{i\in I}{h}_i$

for $k=1$ to$m$ do

$G_L\leftarrow 0,H_L\leftarrow 0$

for $j in sorted\left(I,by x_{jk}\right)$ do                                                $G_L\leftarrow G_L+g_j,H_L\leftarrow H_L+h_j$                                                $G_R\leftarrow G-G_L,H_R\leftarrow H-H_L$                                  $score\leftarrow max\left(score,\frac{G_L^2}{H_L+\lambda }+\frac{G_R^2}{H_R+\lambda }-\frac{G^2}{H+\lambda }\right)$

end

end

Output: Split with max score