Pseudo Code for Sample Auxiliary and OnePass Algos.

approx_alg.tex

@@ -84,6 +84,52 @@ For the running example, after the first pass, \textit{Sample} would have learne
 
 \subsubsection{Psuedo Code}
 
+\begin{algorithm}
+	\caption{OnePass($\polytree$)}
+	\label{alg:one-pass}
+\begin{algorithmic}[1]
+	\State $acc \gets 0$
+	\If{$\polytree.head.val == "+"$}
+		\For{$child$ in $T.children$}
+			\State $acc = acc + OnePass(child)$
+		\EndFor
+		\State $T.partial \gets acc$
+		\For{$child$ in $T.children$}
+			\State $child.weight = \frac{child.c_i}{T.partial}$
+		\EndFor
+		\State Return $T.partial$
+	\ElsIf{$T.head.val == "\times"$}
+		\State $acc \gets 1$
+		\For{$child$ in $T.children$}
+			\State $acc = acc \times= OnePass(child)$
+		\EndFor
+		\State $T.partial \gets acc$
+	\Else
+		\State Return $T.c_i$
+	\EndIf
+\end{algorithmic}
+\end{algorithm}
+
+\begin{algorithm}
+	\caption{Sample($\polytree$)}
+	\label{alg:sample}
+	\begin{algorithmic}[1]
+		\If{$T.head.val == "+":$}
+			\State $T_{samp} \gets$ WeightedSample($T.children$, $T.weights$)
+			\State $Sample(T_{samp})$
+		\ElsIf{$T.head.val == "\times":$}
+			\State $c_i = 1$
+			\State $monom \gets ""$
+			\For {$child$ in $T.children:$}				
+				\State $monom = monom ++ Sample(child)\_1$
+				\State $c_i = c_i \times Sample(child)\_2$
+			\EndFor
+		\Else
+			\State Return $(T.head.val, 1 \times T.c_i)$
+		\EndIf
+	\end{algorithmic}
+\end{algorithm}
+
 \subsubsection{Correctness}
 
 \subsubsection{Run-time Analysis}

main.tex

@@ -2,6 +2,7 @@
 \documentclass[sigconf]{acmart}
 
 \usepackage{algpseudocode}
+\usepackage{algorithm}
 
 \usepackage{comment}
 \usepackage{amsmath}