# hamiltonian-cycle

##### Complete Weighted Graph and Hamiltonian Tour

I ran into a question on a midterm exam. Can anyone clarify the answer? Problem A: Given a Complete Weighted Graph G, find a Hamiltonian Tour with minimum weight. Problem B: Given a Complete Weighted Graph G and Real Number R, does G have a Hamiltonian Tour with weight at most R? Suppose there is a machine that solves B. How many times can we call B (each time G and Real number R are given),to solve problem A with that machine? Suppose the sum of Edges in G up to M. 1) We cannot do this, because there is uncountable state. 2) O(|E|) times 3) O(lg m) times 4) because A is NP-Hard, This is

2021-06-14 20:30:19    分类:问答    algorithm   graph   computation-theory   np   hamiltonian-cycle

##### Find shortest path from X,Y coordinates (with start ≠ end)

I have a dataframe with X and Y coordinates of points like this: structure(list(X = c(666L, 779L, 176L, 272L, 232L, 74L, 928L, 667L, 1126L, 919L), Y = c(807, 518, 724, 221, 182, 807, 604, 384, 142, 728)), .Names = c("X", "Y"), row.names = c(NA, 10L), class = "data.frame") I just want to find out the shortest path connecting all these points, and also return its total distance. There are no other conditions: every point can be connected to any other, no specific point to start or end, no weights, etc... I found lots of topics about igraph package but i can't figure out how to feed my data into

2021-06-11 00:36:06    分类:问答    r   igraph   traveling-salesman   hamiltonian-cycle

##### 在 DAG 中寻找汉密尔顿路径的算法(Algorithm for finding a Hamilton Path in a DAG)

2021-06-10 03:15:11    分类:技术分享    algorithm   graph-algorithm   directed-acyclic-graphs   hamiltonian-cycle

##### Algorithm to find a random Hamiltonian path in a grid?

I'm looking for an efficient algorithm that is able to find an as random as possible Hamiltonian path in a bidirectional N*M grid. Does anyone know where I can find, or how to go about constructing such an algorithm? I've already found an efficient approach (see image below). The end result here is a Hamiltonian cycle. Removing a random edge will make it a Hamiltonian path. This algorithm is efficient, but does not provide enough randomness. This approach will always have the begin and end point of the path right next to each other, while I'd like to have those in random locations. Space

2021-05-31 12:20:26    分类:问答    algorithm   graph-algorithm   hamiltonian-cycle

##### 在图中找到哈密顿循环的动态编程算法是什么？(What is the dynamic programming algorithm for finding a Hamiltonian cycle in a graph?)

2021-05-17 23:24:47    分类:技术分享    algorithm   graph   cycle   dynamic-programming   hamiltonian-cycle

##### 骑士的巡回路线实现选择步长数组(Knight's tour backtrack implementation choosing the step array)

2021-04-30 08:22:00    分类:技术分享    c++   algorithm   backtracking   hamiltonian-cycle

##### What is the dynamic programming algorithm for finding a Hamiltonian cycle in a graph?

What is dynamic programming algorithm for finding a Hamiltonian cycle in an undirected graph? I have seen somewhere that there exists an algorithm with O(n.2^n) time complexity.

2021-04-22 19:20:46    分类:问答    algorithm   graph   cycle   dynamic-programming   hamiltonian-cycle

##### Algorithm for finding a Hamilton Path in a DAG

I am referring to Skienna's Book on Algorithms. The problem of testing whether a graph G contains a Hamiltonian path is NP-hard, where a Hamiltonian path P is a path that visits each vertex exactly once. There does not have to be an edge in G from the ending vertex to the starting vertex of P , unlike in the Hamiltonian cycle problem. Given a directed acyclic graph G (DAG), give an O(n + m) time algorithm to test whether or not it contains a Hamiltonian path. My approach, I am planning to use DFS and Topological sorting. But I didn't know how to connect the two concepts in solving the problem

2021-04-22 11:25:47    分类:问答    algorithm   graph-algorithm   directed-acyclic-graphs   hamiltonian-cycle

##### Knight's tour backtrack implementation choosing the step array

So I came up with this implementation for solving knights tour for a 8*8 chess board. But seems like it is taking a long time running (so long that I have to stop it). But if I replace the dx, dy arrays with the one written in comments and the program works like magic and gives the output. They say that it is cleverly choosing the array, so that the bruteforce algo is lucky to find the solution quickly. But how does one come up with this array at first place, this array (dx,dy) I got from some other code. So can anyone explain me why does this code work with those arrays (in comment) and not

2021-04-05 08:23:00    分类:问答    c++   algorithm   backtracking   hamiltonian-cycle