3. (10 points) A seven-segment display indicates a single decimal digit as a subset of lighted segments labeled A through G as shown below, where a 1 in the table indicates that the corresponding segment is on, and a 0 indicates it is off. Unfortunately, the display is very dim, so that you must focus on a single segment at a time to determine whether it is really on or off. You would like to determine the intended displayed digit by checking the fewest possible number of segments in the worst case. Construct a binary decision tree of minimum height representing your algorithm, labeling: each internal vertex with a letter A through G indicating which segment to check. each edge with a 0 (left) or 1 (right) indicating the state of the checked segment. each leaf with the "output" digit 0 through 9. 0 123456789 A F B ABCDEEG 0 1 1 0 1 1 1 1 1 G 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 E C 1 0 1 0 0 0 1 0 1 0 F 1 0 0 0 1 1 1 0 1 1 D 0 0 1 1 1 1 1 0 1 1