hamiltonian-cycle

Knight's tour backtrack implementation choosing the step array

由 百般思念 提交于 2020-04-25 10:51:32
问题 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

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

由 别来无恙 提交于 2020-01-14 03:17:32
问题 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

Given some words, find a sequence such that any adjacent words of the seq cannot have same characters

由 你。 提交于 2019-12-25 14:00:28
问题 Given some words, e.g. banana , cat , dog, elephant, type, middle, lake find a sequence such that (1) every word is on the sequence (2) any adjacent words cannot have same characters. If the seq cannot be found, return false. otherwise, return true and the seq. No duplicated. No permutations of words. My idea: Set up a graph, and use Hamiltonian path to find the seq. But, it is a NP complete. How to avoid Hamiltonian path ? Any better ideas ? thanks 回答1: Note that if you have constructed a

Checking if a Hamilton Cycle exists in a dense graph

由 孤人 提交于 2019-12-24 00:36:36
问题 A few definitions first: Definition 1 A graph G = (V, E) is called ``dense'' if for each pair of non-adjacent vertices u and v, d(u) + d(v)>=n where n = |V| and d(*) denotes the degree of the vertex * Definition 2 A ``Hamiltonian cycle'' on G is a sequence of vertices ( vi1, vi2,....vin, vi1 ) such that vil != vih for all l!=h and { vil, vil} is an edge of G. The problem is: write a program that, given a dense undirected graph G = (V; E) as input, determines whether G admits a Hamiltonian

Algorithm for finding a Hamilton Path in a DAG

由 本秂侑毒 提交于 2019-12-18 10:34:25
问题 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

Detect cycles in undirected graph using boost graph library

由 こ雲淡風輕ζ 提交于 2019-12-14 03:49:01
问题 I've been stuck since yesterday with this problem. Unfortunately/fortunately this problem makes only about 0.5% of the my super huge (for me, a c++ newbie) algorithm thus the need for a library of existing code that one can just adapt and get things working. I'll like to detect and give out all the circles in an undirected graph. My edges are not weighted. Yes, what I need is really all the cycles i.e. somthing like all the hamiltonian cycles of a directed graph I've been playing aroung with

Complete Weighted Graph and Hamiltonian Tour

由 笑着哭i 提交于 2019-12-09 16:46:47
问题 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,

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

由 蹲街弑〆低调 提交于 2019-12-08 18:24:35
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

Finding all hamiltonian cycles

由 可紊 提交于 2019-12-07 17:28:03
问题 I'm trying to implement a method for adding all possible Hamiltonian cycles to a list using recursion. So far my stopping condition isn't sufficient and I get "OutOfMemoryError: Java heap space" in the line that adds a vertex to a list: private boolean getHamiltonianCycles(int first, int v, int[] parent, boolean[] isVisited, List<List<Integer>> cycles) { isVisited[v] = true; if (allVisited(isVisited) && neighbors.get(v).contains(new Integer(first))) { ArrayList<Integer> cycle = new ArrayList<

Palmer's Algorithm for Hamiltonian cycles

由 。_饼干妹妹 提交于 2019-12-06 06:30:50
问题 In a "dense" graph, I am trying to construct a Hamiltonian cycle using Palmer's Algorithm. However, I need more explanation for this algorithm because it does not work with me when I implement it. It seems that there is an unclear part in Wikipedia's explanation. I would be thankful if someone explains it more clearly or give me some links to read. Here's the algorithm statement: Palmer (1997) describes the following simple algorithm for constructing a Hamiltonian cycle in a graph meeting Ore
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