Question

Derive the Big O running time of Dijkstra algorithm. Please show work

Answer 1

Djkstsa algovith is used to tind the destination to Stayting node shostest node by exchang ing values with neighbouy nodes. If adjust nodes to B, C are and shortest distance to find A Want only possible to D from A It B and c'ase then it gets Paths both distance for to select two paths thoough C, B. and Uses best one- Same way qhe node In the calculate shortest path to all nodes other Yemaing nodes.

Big d calculating the Yunning time for Now we aye algoyithm Dijkstra time step bt step proceduce to find sig-o vertices total number 1) Let the of in di is "v" 2) In connected Vestex Every gYaph adjacent edejes otheyx is (-D · 15 connected to all adj acent v-1 xedges have EVery edge means 3) In minimum heap for finding and weight of updating adjacent veytex is each oClogen)+ o() osdey of DU) is negligible Hexe both steps 2, and 3; complexity foy the time a vertex to update all adjacent veytices is (E* log v) 5) (E* logv) is for single vertex: but we have V vertexs SO V(E* Logy).

(AGeI +3)^ time complexity for Dijkstra is the big o of all to exchange values algoyithm - to all other remaing verte x veytex djusent time complexity =v CE *log v) Bigo Dij kstya V=numbey af vertex. where E- humber of vertex -1