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Problem 3 (4 points). For the graph $G = (V, E)$ with weight $w: E \rightarrow \mathbb{R}_{>0}$ in Figure 1: 1. Use Dijkstra's algorithm to compute the shortest paths from a to all other vertices; 2. Use Prim's algorithm to find the minimum spanning tree, with a being the root vertex. a 9 f 8 12 6 5 b 29 g 2 e 7 14 15 16 c 31 d Figure 1: $G = (V, E)$ You can use the Table 1 and Table 2 to describe the execution of two algorithms respectively. iterations vertices considered b c d e f g d$\pi$ d$\pi$ d$\pi$ d$\pi$ d$\pi$ d$\pi$ 1 a 8 a $\infty$ / $\infty$ / $\infty$ / 9 a 12 a 2 b 3 4 5 6 7 Table 1: Running Dijkstra's algorithm on the graph in Figure 1.

          Problem 3 (4 points). For the graph $G = (V, E)$ with weight $w: E \rightarrow \mathbb{R}_{>0}$ in Figure 1:
1. Use Dijkstra's algorithm to compute the shortest paths from a to all other vertices;
2. Use Prim's algorithm to find the minimum spanning tree, with a being the root vertex.
a
9
f
8
12
6
5
b
29
g
2
e
7
14
15
16
c
31
d
Figure 1: $G = (V, E)$
You can use the Table 1 and Table 2 to describe the execution of two algorithms respectively.
iterations
vertices
considered
b
c
d
e
f
g
d$\pi$
d$\pi$
d$\pi$
d$\pi$
d$\pi$
d$\pi$
1
a
8
a
$\infty$
/
$\infty$
/
$\infty$
/
9
a
12
a
2
b
3
4
5
6
7
Table 1: Running Dijkstra's algorithm on the graph in Figure 1.

Problem 3 (4 points). For the graph G = (V, E) with weight w: E →ℝ>0 in Figure 1:
1. Use Dijkstra's algorithm to compute the shortest paths from a to all other vertices;
2. Use Prim's algorithm to find the minimum spanning tree, with a being the root vertex.
a
9
f
8
12
6
5
b
29
g
2
e
7
14
15
16
c
31
d
Figure 1: G = (V, E)
You can use the Table 1 and Table 2 to describe the execution of two algorithms respectively.
iterations
vertices
considered
b
c
d
e
f
g
dπ
dπ
dπ
dπ
dπ
dπ
1
a
8
a
∞
/
∞
/
∞
/
9
a
12
a
2
b
3
4
5
6
7
Table 1: Running Dijkstra's algorithm on the graph in Figure 1.

Added by Christopher C.

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