The council shall prescribe that sidewalks[,] except crosswalks, shall be built by the owner of platted land within the city in the public streets adjacent to and abutting upon such lots and premises in the manner and within the time to be prescribed by ordinances; provided that, in case of the failure of any such owner to comply with the provisions of such ordinance[,] the city may build or cause to be built such sidewalks and assess the cost thereof against such owner and against the land improved thereby, in a manner prescribed by the council by ordinance.