test case will consist of a sequence of edge descriptions followed by a pair of zeroes each edge description will consist of a pair of integers;
The first integer identifies the node from which the edge begins, and the second integer identifies the node to which the edge is directed. node numbers will always be greater than zero.
OutputFor each test case display the line "case K is a tree. "or the line" case K is not a
connectivity issues for graphs: the connected component and spanning tree of undirected graphs, all vertices are by edges connected together, but There is no diagram of the loop. Figure g= (V, E) is a connected graph that divides the edge set E (g) into two sets of T (g) and B (g) When traversing the graph G from any vertex of the
]=maxint means s to v without direct edge
dis[s]=0; S={s}; s represents a set of points that have been expanded
For I:=1 to N-1 does take a vertex u out of the v-s to expand,
Requirements: Dis[u]=min{dis[v]|v∈v-s}//Here is also the key to the algorithm, S to u shortest path d[u] is no longer small. You can use heap optimization here.
S=s+{u}
Each side of the for U connection
Relax (U,V)
No heap optimization O (v^2) recommended dense
In the previous introductory diagram article, we learned that graph is an abstract representation of the relationship between things, and based on the concept of graphs, we take out all the non-loop graphs and give them a new name-the tree.There are a lot of conceptual terms about trees, so let's start with a simple two-fork tree (a root with up to two subtrees) for analysis.This is some simple two-fork
algorithms and data structures. Make a note so that you do not forget to think about it for a long time. If you encounter a string problem, it generally does not exceed the range of these methods. Let's take a look at the figure, which mainly describes the relationship between the data structures of these algorithms. The yellow part in the figure mainly describes the key points of these algorithms and data structures.
As shown in the figure, the relationship is as follows: Extend-KMP is the e
Deep search and wide search of graphsReview the next two tree, the deep search and wide search.From the graph's traversal. There are two ways to traverse a graph: depth-first traversal (Depth, first search), breadth-priority traversal (breadth-search), its classic application maze, n-Queen, binary tree traversal, and so on. Traversal is to access all the nodes in
algorithms and data structures. Make a note so that you do not forget to think about it for a long time. If you encounter a string problem, it generally does not exceed the range of these methods. Let's take a look at the figure, which mainly describes the relationship between the data structures of these algorithms. The yellow part in the figure mainly describes the key points of these algorithms and data structures.
As shown in the figure, the relationship is as follows: Extend-KMP is the e
This document lists: one, time module; second, dictionary and hash hash table; Third, the realization of the graph and the tree; Iv. member query; Insert ObjectOne, timing module (Timeit, CProfile)import timeittimeit.timeit(‘x = 1 + 2‘)Since learning the algorithm, it is important to calculate the time spent on the program, but it should be noted that: the Timeit () Timing function runs the relevant code sn
As we have said in the definition of graphs, a graph with a power value is a net structure. The spanning tree of a connected graph is a minimal connected subgraph, which contains all the vertices of the graph, but only enough to form a n-1 edge of a tree. The so-called minim
Tree charts and graphs are one of the most common questions during the interview.
Key points:
1. Tree, binary tree, binary search tree, binary seach tree, defined.
2. binary tree traversal: Preorder, inorder, and postorder. Layere
Preface
This blog introduces and queries the set and the Minimum Spanning Tree of the graph. For the query set, we introduce its basic concepts, analyze its complexity, and finally use the query set to analyze the Minimum Spanning Tree. And query the reference documents 《
Algorithm Introduction: Blog: http://blog.csdn.net/dm_vincent/article/details/7655764. The
In the previous introductory diagram article, we learned that graph is an abstract representation of the relationship between things, and based on the concept of graphs, we take out all the non-loop graphs and give them a new name-the tree.There are a lot of conceptual terms about trees, so let's start with a simple two-fork tree (a root with up to two subtrees) for analysis.This is some simple two-fork
the explicit children field, do not need to set the VIS array to ensure that only one traversal, because the knowledge is convenient once.Travel (node) {for (I=1:lengh) { //..... Process node Node if (null! =children) Travel (children); Another way of writing is to write a for loop outside the functionthe hierarchical traversal of the tree and BFS is very similar, in general is the DFS stack, is not the stack is impl
The minimum spanning tree can have multiple in a graph, but if the weights of the edges in a graph are different, then the smallest spanning tree may only exist, and it is easy to prove it with contradiction.Of course the minimum spanning tree is also a
Today is the end of the big picture, the last thing of "figure", "minimum spanning tree" and "Shortest path".
One: Minimum spanning tree
1. The concept
First look at the following figure, do not know what you can sum up.
For a connected graph G, if all its vertices and portions of the edges constitute a subgraph G1, when G1 satisfies:
① just connects all the
Description
Given a connected undirected graph, tell if it minimum spanning is unique.
Definition 1 (Spanning tree): Consider a connected, undirected graph G = (V, E). A spanning tree of G are a subgraph of g, say T = (V ', E '), with the following properties:
V ' = v.
T is connected and acyclic.
Definition 2 (Minimum
The Minimum Spanning Tree of an undirected graph G is a tree composed of the edges of all vertices connected to g in the graph, and its total weight is the lowest. The Minimum Spanning Tree exists when and only when G is connected.
If an edge e that does not belong to T is a
1. Data structure for edges with weights
/** * This class of objects can represent an edge in the graph * @author lhever February 19, 2017 pm 5:10:49 * @version v1.0 */public class Edge implements comparable
2 Weighted Graph-free data structure
Import java.util.ArrayList;
Import java.util.List;
public class Edgeweightedgraph {private static final String NEWLINE = System.getproperty ("Lin
Topic:Given n nodes labeled from 0 n - 1 to and a list of undirected edges (each edge is a pair of nodes), write a funct Ion to check whether these edges make up a valid tree.For example:Given n = 5 edges = [[0, 1], [0, 2], [0, 3], [1, 4]] and, return true .Given n = 5 edges = [[0, 1], [1, 2], [2, 3], [1, 3], [1, 4]] and, return false .Hint:
Given n = 5 edges = [[0, 1], [1, 2], [3, 4]] and, what should your return?Is this case a valid tree? S
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