Question

Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST) with node 1 as the "root". List the vertices in the order in which the algorithm adds them to the solution, along with the edge and its weight used to make the selection, one per line. Each line should look like this: add vertex y: edge = (x,y), weight = 5 When the algorithm ends there are, generally, edges left in the heap. List all the leftover edges, expressing each such edge as an ordered pair.

Answer 1

Prism's Algorithm:_*) followed greedy method *) setet start with Starting usbesc seleeting min weight until all istices covered, no cycle forned ok) DIf graph have investices msT hare CD-Dedag

Prism's olgantam- to start with Vertexty with min reput bash Table - 0 = 1 add versc ua (VN)=1 2-next min necht ( =3 o addrester v8 CVI, VG) 23 3. next min neint 6-4 o add vertesc V7 CV, V7)=4 Vg - V7=9 -18=12 Vz-v4=15 4-15-18 15-16=19 Verve=20 V6-6-6 V6-v=1 VG-12=7 며 4 next man neht 17-V676 add rotecro (7,16)76 5-neset min weht 12-16=7 {cycle Jazz V-3=11 add uste (3) (6 kan 6 next min Leht - =15 add ists(/4) CLS 4025 (18) 69

7 not corsed restex is us with min nesant y =18 ♡ 15 add verse is cvar/33=18 fincu MST 1+3+4+6+7+15+18 = 54 Leftover edges - * ®=13 20-9:♡ ♡ =14; *'** ;-07 o o 19 ; 6 =20 7 edges in mst 7 edges not in mot

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