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  • Traveling Salesman Problem is one of the most intensively studied problems in computational mathematics. Travelling Salesman problem is a problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. Travelling Salesman Problem was invented by Hassler Whitney at Princeton. In the 1950s and 1960s, the problem became increasingly popular in scientific circles in Europe and the USA. These problems will be solved with depth first search algorithm and using tree data structures. Depth First Search is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization