2025-005

A salesperson wants to plan their route between five cities — A, B, C, D, and E — using the Farthest Insertion algorithm.

The initial cycle considered is B–D–E–B, highlighted in dark blue in the figure below.

The distances between cities (in arbitrary units) are indicated on the edges of the graph:


Map of cities and distances

Applying the Farthest Insertion algorithm, determine:

  1. The order of insertion of cities outside the initial cycle (A and C).

  2. The final cycle resulting after all insertions.

A) Order: A, C → Final cycle: B–A–D–C–E–B
B) Order: C, A → Final cycle: B–D–C–E–A–B
C) Order: C, A → Final cycle: B–C–D–E–A–B
D) Order: A, C → Final cycle: B–D–E–C–A–B
E) None of the above


Original idea by: Giancarlo Maldonado Cárdenas

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