let and denote the number of vertices and edges of the input graph grespectively the implementation issues for the prim-jarnik algorithm are similar to those for dijkstra' algorithm if we implement the adaptable priority queue as heap that supports location-aware entries (section )then we can extract the vertex in each iteration in (log ntime in additionwe can update each [zvalue in (log ntimeas wellwhich is computation considered at most once for each edge ( ,zthe other steps in each iteration can be implemented in constant time thusthe total running time is (( +mlog )which is ( log nillustrating the prim-jarn ik algorithm we illustrate the prim-jarn ik algorithm in figures through figure an illustration of the prim-jarnik mst algorithm (continues in figure