Whenever a state highway crosses or shall hereafter cross one or more railroads, and whenever the Idaho transportation department shall determine that the elimination of a grade crossing, whether by separation of grades or by relocation of the highway or railroad or both, or the reconstruction of an existing structure under or over the railroad or railroads, is necessary for public safety and convenience or for the proper construction or reconstruction of said state highway, the said Idaho transportation department shall have full authority to negotiate with and enter into an agreement with the railroad company or companies, and with any other persons and authorities concerned, to provide for the method of elimination or alteration and for the division of the cost thereof between the state and the railroad company or companies and any other parties to such agreement, such cost to include all changes of highway or railroads made necessary by the existence of the crossing and by the elimination or alteration thereof, and the acquisition of any right of way required therefor.