Math

QuestionUse the nearest neighbor algorithm on the graph with edge weights given. Start and end at vertex A. List the vertices.

Studdy Solution

STEP 1

Assumptions1. The table represents the weights of the edges in a graph. . We are starting from vertex A.
3. The nearest neighbor algorithm is used to find the shortest path.

STEP 2

The nearest neighbor algorithm starts at a given vertex and selects the vertex closest to the current vertex at each step. So, we start at vertex A.

STEP 3

Looking at the row for vertex A in the table, the nearest vertex (smallest weight) is vertex C with a weight of.
ACA \rightarrow C

STEP 4

Next, we look at the row for vertex C in the table, excluding vertex A which we have already visited. The nearest vertex is vertex F with a weight of27.
ACFA \rightarrow C \rightarrow F

STEP 5

Next, we look at the row for vertex F in the table, excluding vertices A and C which we have already visited. The nearest vertex is vertex with a weight of1.
ACFA \rightarrow C \rightarrow F \rightarrow

STEP 6

Next, we look at the row for vertex in the table, excluding vertices A, C, and F which we have already visited. The nearest vertex is vertex D with a weight of15.
ACFDA \rightarrow C \rightarrow F \rightarrow \rightarrow D

STEP 7

Next, we look at the row for vertex D in the table, excluding vertices A, C, F, and which we have already visited. The nearest vertex is vertex B with a weight of43.
ACFDBA \rightarrow C \rightarrow F \rightarrow \rightarrow D \rightarrow B

STEP 8

Finally, we have visited all vertices except for A. So, we return to A.
ACFDBAA \rightarrow C \rightarrow F \rightarrow \rightarrow D \rightarrow B \rightarrow AThe shortest path using the nearest neighbor algorithm starting at vertex A is ACFEDBA.

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