Navigation apparatuses, methods, and programs store path information for a path each time the path is traveled, the path being a segment of the guidance route from a branch point to a junction. The apparatuses, methods, and programs store detour route information for the detour route each time the detour route is traveled. The apparatuses, methods, and programs receive current traffic conditions from an external system and read out, when arriving at the branch point, path information having a same or similar stored traffic condition as a current path traffic condition and detour route information having a same or similar stored traffic condition as a current detour route traffic condition. The apparatuses, methods, and programs determine a difference between a required time for traveling along the path and a required time for traveling along the detour route and output guidance information based on the determined difference.