$(25$ points$)$ You are given the locations of $n$ buildings $B_1,$dots,$B_n$ on the real line. Each location is a coordinate $($i$.$e$.,$ a real number$).$ Each building $B_i$ has a WIFI signal receiver with a range of $r_i>0.$ That is$,$ if we place a signal tower at distance $r_i$ or less from $B_i,$ then $B_i$ gets WIFI. Note that the signal receivers of different buildings may have different ranges.

Describe a greedy algorithm that places the smallest number of signal towers so that every building gets WIFI. Explain the correctness of your algorithm. Derive the running time of your algorithm.