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Question
hamiltonian cycle using backtracking algorithmhamiltonian cycle algorithm using backtracking pdfhamiltonian path algorithmhamiltonian cycle examplehamiltonian cycle in daa algorithmhamiltonian cycle np-completehamiltonian path leetcodehamiltonian path problem in toctime complexity of graph coloring using backtrackingtime complexity of travelling salesman problem using branch and boundReport inappropriate predictions
Solution
Sure, I can help you with that. Here are the steps to find a Hamiltonian cycle using the backtracking algorithm:
- Start with an empty path and an empty set of visited vertices.
- Choose a starting vertex.
- Add the starting vertex to the path and mark it as visited.
- If all vertices are visited and the last vertex is adjacent to the starting vertex, then a Hamiltonian cycle is found. Print the cycle and return.
- If all vertices are visited but the last vertex is not adjacent to the starting vertex, backtrack by removing the last vertex from the path and marking it as unvisited.
- If all vertices are not visited, choose a vertex adjacent to the last added vertex that has not been visited yet.
- Repeat steps 4 to 6 until a Hamiltonian cycle is found or all possibilities are exhausted.
I hope this helps! Let me know if you have any further questions.
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raveling Salesman Problem 推销员问题这个问题仅仅是指数时间复杂度问题的例子，此处不要求理解和掌握，只要记住推销员问题可以是指数时间复杂度即可。Input: There are n cities.Output: Find the shortest tour from a particular city that visit each city exactly once beforereturning to the city where it started (Hamiltonian circuit).A Hamiltonian circuit can be represented by a sequence of n+1 cities v1 , v2 , …, vn , v1 , where thefirst and the last are the same, and all the others are distinct.Exhaustive search approach: Find all tours in this form, compute the tour length and find theshortest among them按照上面这种思路，一共要考虑 种不同的路线（指数时间复杂度）。Knapsack Problem 背包问题这个问题仅仅是指数时间复杂度问题的例子，此处不要求理解和掌握，只要记住背包问题可以是指数时间复杂度即可。Input: Given n items with weights w1 , w2 , …, wn and values v1 , v2 , …, vn , and a knapsack withcapacity W.Output: Find the most valuable subset of items that can fit into the knapsack.Application: A transport plane is to deliver the most valuable set of items to a remote locationwithout exceeding its capacityExhaustive search approach: Try every subset of the set of n given items, compute total weight ofeach subset and compute total value of those subsets that do NOT exceed knapsack's capacity按照上面这种思路，一共要考虑 种不同的路线（指数时间复杂度）。for i = 1 to n-1 dobeginkey = a[i]pos = 0while (a[pos] < key) && (pos < i) dopos = pos + 1shift a[pos], …, a[i-1] to the righta[pos] = keyend
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