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Traveling Salesman Problem 9 Cities
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A synapse is the tiny gap where one neuron passes information to the next.

Your brain stores knowledge in neuron connections called synapses. When those connections or links fade, you forget.
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Adjacency Matrix Visualizer + Deterministic Path Engine

The Traveling Salesman Problem (TSP) and Hamiltonian Path/Cycle problems are closely related, but they are not the same thing.

Travelling Salesman Problem — Route Count Formulas

In a travelling salesman problem with 9 cities, the goal is to find the shortest possible route that starts at City A, visits each of the remaining eight cities exactly once, and returns to City A.

Directed Graph (Ordered Routes)

The number of possible directed tours is given by: 

P(n) = (n − 1)!

For nine cities: 

P(9) = 8! = 40,320

Undirected Graph (Unique Routes)

In an undirected TSP, a route and its reverse direction represent the same path. To remove these duplicates, the number of unique tours is: 

U(n) = (n − 1)! / 2

For nine cities: 

U(9) = 8! / 2 = 20,160

This means there are 20,160 unique undirected tours when reverse paths are treated as identical.


Explainable AI Diagram

Click any cell to edit its weight. Use 1e9 to mark a forbidden transition.

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Matrix JSON

Reasoning trace