1. A navigation system for searching a route to a destination and guiding a vehicle to the destination, the navigation system comprising: a road map data storage unit storing road map data including altitude information; an energy variation calculation unit programmed to calculate a variation of mechanical energy of the vehicle travelling on a road link included in the road map data; and a route-search unit programmed to search for a fuel-efficient route for the vehicle based on the variation of mechanical energy calculated by the energy variation calculation unit; a display unit programmed to display the fuel-efficient route for the vehicle; wherein the energy variation calculation unit is further programmed to: divide the road link to be used for route-searching into a plurality of sub-links each approximated by a line segment; calculate the variation of mechanical energy of the vehicle travelling on the plurality of the sub-links in an acceleration travel mode, a deceleration travel mode, and a constant-speed travel mode, wherein each of the variations of mechanical energy includes a total variation of friction energy based on a length of each sub-link calculated from coordinate information, potential energy based on an altitude difference of both ends of each sub-link calculated by the coordinate information including the altitude information, and kinetic energy; categorize the sub-links in accordance with an estimated fuel consumption in each of the acceleration travel mode, the deceleration travel mode, and the constant-speed travel mode into a first category in which the estimated fuel consumption is equal to a minimum fuel consumption of the vehicle in all of the acceleration, deceleration and constant-speed travel modes, a second category in which the estimated fuel consumption is not equal to the minimum fuel consumption in the acceleration travel mode but is equal to the minimum fuel consumption in the deceleration and constant-speed travel modes, a third category in which the estimated fuel consumption is not equal to the minimum fuel consumption in the acceleration and constant-speed travel modes but is equal to the minimum fuel consumption in the deceleration travel mode, or a fourth category in which the estimated fuel consumption is not equal to the minimum fuel consumption in all of the acceleration, deceleration and constant-speed travel modes; calculate a sum of the variations, per each categorized sub-link, of mechanical energy that is the total variation of friction energy, potential energy, and kinetic energy of the vehicle travelling on the plurality of sub-links of the road link; and render the sum calculated per each categorized sub-link as a geometry parameter of the road link and stores the geometry parameter in a geometry parameter storage unit; wherein the route-search unit is programmed to use the geometry parameters in searching for the fuel-efficient route.