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Answer :
Sure! Let's apply the nearest neighbor algorithm starting from vertex A.
1. Start at Vertex A: We begin at vertex A and will look for the closest vertex (smallest weight) that hasn't been visited yet.
2. Find Nearest Neighbor from A:
- Look at the row for A: {B: 3, C: 27, D: 14, E: 45, F: 43}
- The nearest neighbor is B with a weight of 3. So, we go from A to B.
3. Move to Vertex B: Now we are at B. Find the nearest unvisited neighbor.
- Look at the row for B: {A: -, C: 8, D: 31, E: 21, F: 19}
- The nearest neighbor is C with a weight of 8. So, we go from B to C.
4. Move to Vertex C: Now we are at C. Find the nearest unvisited neighbor.
- Look at the row for C: {A: 27, B: -, D: 2, E: 48, F: 46}
- The nearest neighbor is D with a weight of 2. So, we go from C to D.
5. Move to Vertex D: Now we are at D. Find the nearest unvisited neighbor.
- Look at the row for D: {A: 14, B: 31, C: -, E: 60, F: 44}
- The nearest neighbor is F with a weight of 44. So, we go from D to F.
6. Move to Vertex F: Now we are at F. Find the nearest unvisited neighbor.
- Look at the row for F: {A: 43, B: 19, C: 46, D: 44, E: 33}
- The nearest neighbor is E with a weight of 33. So, we go from F to E.
7. Move to Vertex E: Now we are at E. We have visited all vertices, so we return to the starting vertex A.
- Go back to A with a weight of 45.
This completes our tour. The entire path using the nearest neighbor algorithm is A → B → C → D → F → E → A.
The sequence of vertices gives us the result: ABCDFEA.
1. Start at Vertex A: We begin at vertex A and will look for the closest vertex (smallest weight) that hasn't been visited yet.
2. Find Nearest Neighbor from A:
- Look at the row for A: {B: 3, C: 27, D: 14, E: 45, F: 43}
- The nearest neighbor is B with a weight of 3. So, we go from A to B.
3. Move to Vertex B: Now we are at B. Find the nearest unvisited neighbor.
- Look at the row for B: {A: -, C: 8, D: 31, E: 21, F: 19}
- The nearest neighbor is C with a weight of 8. So, we go from B to C.
4. Move to Vertex C: Now we are at C. Find the nearest unvisited neighbor.
- Look at the row for C: {A: 27, B: -, D: 2, E: 48, F: 46}
- The nearest neighbor is D with a weight of 2. So, we go from C to D.
5. Move to Vertex D: Now we are at D. Find the nearest unvisited neighbor.
- Look at the row for D: {A: 14, B: 31, C: -, E: 60, F: 44}
- The nearest neighbor is F with a weight of 44. So, we go from D to F.
6. Move to Vertex F: Now we are at F. Find the nearest unvisited neighbor.
- Look at the row for F: {A: 43, B: 19, C: 46, D: 44, E: 33}
- The nearest neighbor is E with a weight of 33. So, we go from F to E.
7. Move to Vertex E: Now we are at E. We have visited all vertices, so we return to the starting vertex A.
- Go back to A with a weight of 45.
This completes our tour. The entire path using the nearest neighbor algorithm is A → B → C → D → F → E → A.
The sequence of vertices gives us the result: ABCDFEA.
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