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

State travelling salesman problem. How it is related to Hamiltonian circuits?

Describe the traveling salesman problem using dynamic programming and branch and bound

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Is Travelling salesman problem NP-hard or NP-Complete? Justify your answer.

The diagram below shows an input network for the minimum-cost flow problem, and the flow (shown in red) in this network at the end of the 2-nd iteration of the Successive Shortest Path algorithm. During the computation, whenever there is a choice of a vertex, the algorithm selects the vertex which is first in the lexicographical order. (This means, for example, that during the first iteration, the algorithm selected vertex p1 from the two available supply vertices, and selected vertex r1 from the two available demand vertices.) Complete the following statements by dragging and dropping appropriate options.There was  Blank 1 Question 1 path from p2 to r1 in the residual network at the beginning of the 2-nd iteration.At the end of the 2-nd iteration, the flow saturates  Blank 2 Question 1 edges.At the beginning of the 3-rd iteration, the residual supply at vertex p2 is  Blank 3 Question 1 .In the residual network constructed in the 3-rd iteration,  Blank 4 Question 1 vertices are reachable from vertex p2.The cost of the path selected in the residual network in the 3-rd iteration is  Blank 5 Question 1 .The flow in the input network computed by the end of the 3-rd iteration  Blank 6 Question 1 satisfy all supply and demand.