René's URL Explorer Experiment

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It is NP-hard in general."}},{"@type":"Question","url":"https://www.askpython.com/python/examples/travelling-salesman-problem-python#faq-question-1783337810782","name":"Is the greedy algorithm always optimal?","acceptedAnswer":{"@type":"Answer","text":"No. Greedy makes a locally optimal choice at every step and can miss the global optimum. On random inputs it typically lands 10% to 25% above the brute-force optimum."}},{"@type":"Question","url":"https://www.askpython.com/python/examples/travelling-salesman-problem-python#faq-question-1783337810783","name":"When is brute force practical?","acceptedAnswer":{"@type":"Answer","text":"Brute force is practical for n up to about 10 or 11. At n=10 the work is 9! = 362,880 permutations. At n=15 the work is 14! = 87 billion and the loop is no longer a practical option."}},{"@type":"Question","url":"https://www.askpython.com/python/examples/travelling-salesman-problem-python#faq-question-1783337810784","name":"What algorithm should I use for n between 12 and 20?","acceptedAnswer":{"@type":"Answer","text":"Held-Karp dynamic programming in O(n\u00b2 \u00b7 2\u207f) gives the exact answer and runs in seconds for n up to 20. 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