Place cities and watch nearest-neighbor, greedy, and simulated annealing algorithms find short tours. Compare path lengths.
Place cities by clicking the canvas, run the three classic traveling-salesman heuristics - nearest neighbor, greedy edge selection, and simulated annealing - and the tool draws each resulting tour and reports its length so you can compare them. The thing most users misread: this is a heuristic comparison, not an exact solver, so the shortest line on screen is a candidate solution, not a proven optimum. The other surprise is the closing edge: the reported length includes the trip back to the starting city, and that return leg is often what inflates a naive tour.
A concrete input and expected output from the current implementation.
Input
Click four cities onto the canvas at the corners of a square four units on a side: (0,0), (4,0), (4,4), (0,4).
Expected output
Nearest neighbor and greedy both draw the perimeter route and report 16 units; simulated annealing converges on the same tour.
Every side of the square is 4 units and every diagonal is about 5.66, so the perimeter tour, 4 + 4 + 4 + 4 = 16, beats any route that uses a diagonal and is the true optimum. The symmetric layout forces all three heuristics onto the same tour; that agreement is a coincidence of symmetry, not a general guarantee.
Nearest neighbor starts at one city and repeatedly steps to the nearest city not yet visited, closing with the edge back to the start. It is deterministic except when candidates tie, and myopic: each local choice looks safe, yet an early short step can force a long closing edge later. Greedy scans every city pair, accepting the shortest edge that keeps the emerging tour valid until a full tour exists.
Simulated annealing starts from a complete tour and repeatedly tries a small rearrangement, typically swapping the order of two edges, a move known as 2-opt. It accepts every improvement and also some worsening moves, with the acceptance probability shrinking as an annealing temperature cools. That tolerance for uphill steps lets it escape the local minima that trap nearest neighbor; the cost is time, and longer runs usually produce shorter tours.
Nearest neighbor always steps to the closest city and can strand itself with an expensive closing edge; simulated annealing keeps proposing rearrangements and can escape those traps. The gap grows with the number of cities and with elongated or clustered layouts. On small, symmetric layouts the three algorithms often agree, so the difference is easiest to see with more cities.
Probably, but not proven. Agreement is a strong hint on small layouts with a handful of cities, yet heuristics can coincide on a tour that is merely locally optimal. Treat the shortest reported length as a good upper bound on the optimum; only an exact solver can certify that no shorter tour exists.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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