1. A determination tree generating apparatus comprising: an input unit configured to receive a correspondence table showing correspondence between product numbers and component combinations belonging to component categories; a correspondence information generating unit configured to generate first correspondence information corresponding to the correspondence table and including an arrival condition list and the product numbers, the arrival condition list being a sum of sets of arrival conditions as elements each expressing one or more component combinations; a first condition generating unit configured to generate a first arrival condition for a first point of a determination tree, based on one of the correspondence table and the first correspondence information; a provisional determination unit configured to provisionally and sequentially determine all component categories to be classification component categories for the first point, each of the all component categories being used for classification at none of second points that serve as ancestor points of the first point; an assignment/calculation unit configured to assign one of the classification component categories to the first point, and to perform calculation for assigning component names to branches leading from the first point to one or more child points in accordance with the first arrival condition; a second condition generating unit configured to generate a second arrival condition for each of the child points in accordance with the first arrival condition and the calculation; an extracting unit configured to extract, from the first correspondence information, second correspondence information associated with the second arrival condition; an element number calculating unit configured to calculate, for each of the all component categories, number of elements included in an arrival condition list that is included in the second correspondence information; a determining unit configured to determine that one of the all component categories, which corresponds to a minimal number of elements, is a classification component category for the first point, the classification component category being included in the classification component categories; and a point branch generating unit configured to generate a first point assigned to the classification component category, and to generate component names to be assigned to one or more branches leading from the assigned first point to one or more child points, based on a calculation result of the assignment/calculation unit.