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The travelling salesman problem can be solved in

  1. Polynomial time using dynamic programming algorithm
  2. Polynomial time using branch-and-bound algorithm
  3. Exponential time using dynamic programming algorithm or branch-and-bound algorithm
  4. Polynomial time using back tracking algorithm

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As per i know travelling salesman problem is a Np hard not p . if the traveling salesman problem can be solved in polynomial time using backtracking then it will become a P . So its false , it cant be solved in polynomial time by deterministic way .
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