you give undirecte weight connect graph n vertex m edge loop multiple edgesthe ith edge e_i u_i v_i w_i distance vertex u_i v_i edge e_i w_i 1 le w_i the graph connect ie pair vertex path consist edge give grapha minimum span tree mst case positive weight subset edge connect weight undirected graph connect vertex minimum total cost subset total cost sum cost choose edgesyou modify give graph the operation perform follow increase weight edge 1 you increase weight edge multiple possibly zero timessuppose initial mst cost k your problem increase weight edge minimum possible number operation way cost MST obtain graph remain k MST unique mean way choose MST obtain graphyour problem calculate minimum number operation require