I know the answers for each problem, but i'm missing the calculations. Show for every sub-question why this is the case. Answer thoroughly. If you're not planing on giving complete answers or not answering every question, dont even bother.

The algorithm is given below:

2 1 6 2 c d 1 2 f1 2 2 1 Figure 1: The graph G, considered in Problems 3, 4 and 5. Problem 3 (8 %) In this problem we use Dijkstra's algorithm (see Figure 2 on Page 11) on the graph in Figure 1. 1. What is the length of the shortest path from a to 2 (found by Dijkstra's algorithm)? 10 11 12 13 14 2. Which one of the following vertices is added first to the set S od og Oh Di Dj 3. Which one of the following vertices is the last to be added to the set S Oh i j k z What is the weight of a minimum spanning tree of the graph in Figure 1. 19 20 21 22 23 24 25 26 In this problem is the graph in Figure 1. (The edge weights of G are not considered in this problem.) Answer the following true/false problems. G has an Euler circuit G has a Hamilton circuit True True False False What is the number of edges of a spanning tree of G? 01 03 05 07 09 11 13 15 17 What is the degree of the vertex z ? DO 01 2 3 4 5 11 procedure Dijkstra(G: weighted connected simple graph, with all weights positive) {G has vertices a = vO, V1, ...,Vn = ? and lengths w(V;, V;) where w(vi, V;) = if {v;. v;} is not an edge in G} for i:=1 ton L(v;) :=o0 L(a) :=0 S:= y {the labels are now initialized so that the label of a is 0 and all other labels are o, and S is the empty set) while z & S u:= a vertex not in S with L(u) minimal S:= SU {u} for all vertices v not in S if L(u) + w(u, v)