The Travelling Salesman Problem (TSP) is an NP-hard problem.

The **TSP** (Travelling Salesman Problem) has several applications, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing.

Travelling salesman problem can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's length. A TSP tour becomes a Hamiltonian cycle if and only if every edge has the same distance. Often, the model is a complete graph. If no path exists between two cities, adding an arbitrarily long edge will complete the graph without affecting the optimal tour.

** Fig: Symmetric TSP with four cities**

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