Algorithm 1$\mathcal{E}$.

Input: A nonempty decision table T and a number $k\in \{1,\dots ,5\}$. Output: A decision tree of the type k for the table T. Construct a tree G consisting of a single node labeled with T. If no node of the tree G is labeled with a table, then the algorithm ends and returns the tree G. Choose a node v in G, which is labeled with a subtable $\Theta$ of the table T. If $\Theta$ is degenerate, then instead of $\Theta$, we label the node v with 0 if $\Theta$ is empty and with the decision attached to each row of $\Theta$ if $\Theta$ is nonempty. If $\Theta$ is nondegenerate, then depending on k, we choose a query X (either attribute or hypothesis) in the following way: (a)If $k=1$, then we find an attribute X$\in F\left(T\right)$ with the minimum impurity $I(X,\Theta )$. (b)If $k=2$, then we find a hypothesis X over T with the minimum impurity $I(X,\Theta )$. (c)If $k=3$, then we find an attribute Y$\in F\left(T\right)$ with the minimum impurity $I(Y,\Theta )$ and a hypothesis Z over T with the minimum impurity $I(Z,\Theta )$. Between Y and Z, we choose a query X with the minimum impurity $I(X,\Theta )$. (d)If $k=4$, then we find a proper hypothesis X over T with the minimum impurity $I(X,\Theta )$. (e)If $k=5$, then we find an attribute Y$\in F\left(T\right)$ with the minimum impurity $I(Y,\Theta )$ and a proper hypothesis Z over T with the minimum impurity $I(Z,\Theta )$. Between Y and Z, we choose a query X with the minimum impurity $I(X,\Theta )$. Instead of $\Theta$, we label the node v with the query X. For each answer $S\in A\left(X\right)$, we add to the tree G a node $v\left(S\right)$ and an edge $e\left(S\right)$ connecting v and $v\left(S\right)$. We label the node $v\left(S\right)$ with the subtable $\Theta S$ and label the edge $e\left(S\right)$ with the answer S. We then proceed to step 2.