First, the definitionTopological ordering: a sort of vertex with a direction-free graph , which makes the VJ appear behind VI in the sort if there is a path from VI to VJ.The topological ordering of a direction-free graph G is to arrange all the vertices in G into a linear sequence so that any pair of vertices u and V in the graph, and if the Edge Example: In the Learning course map, there is a Second, AOV NetworkIntroduction: An existing project need
-order activity of the end-point activity, Its end-of-activity. Usually, we put this vertex activity, the side represents the relationship between the activities of the graph called vertex activity Network (activity on Vertex Network), referred to as AoV net. Course Code Course name First CourseC1 Advanced Mathematics withoutC2 Programming Basics NoC3 Discrete Mathematics c1,c2C4 data Structure C3,C5C5 algorithm Language C2C6 Compiling technology c4,c
Data structure, data structure and AlgorithmApplication background
Student electivesVertex -- indicates the courseDirected arc -- indicates a prerequisite. If course I is a prerequisite for course j, an arc (I, j) is shown in the figure)In what order should students study these courses in order to complete their studies without conflict and smoothly-topological sorting
A topological sequence is an ordered sequence composed of vertices in a directed acyclic graph. The sequence meets the following
the graph represent the activities (sub-works), the forward side of the graph represents the succession of activities, that is, the activity of the starting point of the edge is the pre-order activity of the end-point activity, Its end-of-activity. Usually, we put this vertex activity, the side represents the relationship between the activities of the graph called Vertex activity Network (activity on Vertex Network), referred to as AoV net. In the
G={v,e} is a direction graph with n vertices, the vertex sequence in V is V1,v2,......, vn, if there is a path from Vertex VI to VJ, vertex VI must precede vertex VJ in vertex sequence. It is said that such a vertex sequence is a topological sequence.
In a direction diagram of a representation project, a vertex is used to represent the activity, and an arc is used to represent the priority relationship between activities, such that a graph is a vertex representing an active network, called a
Topological sorting and key paths are based on Directed Graphs without loops.
It is mainly used to indicate the relationship between events in the project progress.
Topology Sorting and key paths use an adjacent table to store data, and the Minimum Spanning Tree and shortest path use an adjacent matrix to store data.
1. topological sorting
AOV Network: In a directed graph that represents a project, activities are represented by fixed points, and prior
Application backgroundStudent Elective Course QuestionsVertex--Represents a courseArc-Indicates a prerequisite, if course I is a prerequisite for course J, the figure has an arc (I,J)How the students should study these courses in order to complete their studies without contradiction and success--topological sequencing 拓扑序列是有向无环图中各顶点构成的有序序列。该序列满足如下条件:如果图中一顶点vi到另一顶点vj存在一条路径,那么vj在此图的拓扑排序序列中位于vi之后。Directed acyclic graph (DAG) and AoV NetworkDirected a
Topological ordering is not very common, but it should not be underestimated, so also to be careful to do, not sloppy.To define:Topological sorting algorithm, only applicable to AoV network (a direction-free graph). All activities in the AOV network are arranged in a sequence so that all precursor activities of each activity are in front of the activity, which is called "topological ordering", and the resul
Original link: http://blog.csdn.net/wang379275614/article/details/13990163This combination of system Analyst-operations Method-network planning technology-critical Path section, the original link description is not accurate where the correction.Know AoE Network In a direction diagram, a vertex is used to represent an activity, and a forward edge is used to indicate the order in which the activity begins, which is called the AoV (activity on Vertex) n
The main idea is:
The following describes how to sort the topology of an AOV network:
1: select a vertex with an inbound degree of 0 (no direct precursor) from the AOV network and Output
2: delete the vertex from the AOV network and all edges from the vertex.
3: Repeat steps 1 and 2 until the vertex with an input degree of 0 is not found.
There are two kinds of
sequence s, it is divided into two segments, where S1 is already traversed and S2 is not traversed.A data structure is used to store all possible descending sequence segments in the S1, then each time the first element in the S2 is added to the S1, and the S1 all descending sequence segments are modified, the newly generated descending sequence segment is guaranteed to be the new descending sequence segment of S1.Through this idea, can think of using AOV
) and output two integers m and N. said: The system can intercept a maximum of M missiles, if you want to intercept all missiles should be equipped with at least N sets of such missile system. Sample Input300 275 252 138 245Sample OUTPUT5 2First of all, the most intuitive thinking is as follows: Problem translation: This problem is to solve a random sequence of the longest descending sequence thinking: For the target sequence s, divided into two segments, where S1 is already traversed, S2 is not
As we said earlier, topology sequencing is primarily about solving the problem of whether a project can be sequenced, but sometimes we need to solve the problem of the shortest time required to complete the project. If we want to get the shortest time for a flowchart, we have to analyze their topological relationships and find the most critical process, which is the shortest time.
On the basis of the AOV network, we introduce a new concept. In a weig
Previously we mentioned that topological sorting is mainly used to solve the problem of whether a project can be executed sequentially, but sometimes we still need to solve the shortest time required for project completion. If we want to obtain the shortest time for a flowchart, we must analyze their topological relationships and find the most critical process. The shortest time is the shortest time.
Based on the previous AOV network, we will introduc
/*AOV Network (activity on Vertex Network): The graph represents the project: which represents the activity with vertices, and arcs represent the constraints between activities. Is the project going smoothly? ----whether there is a forward loop ******************************************* with the method of generating (including all) vertex sequences in the >aov network, the vertex sequence satisfies: In the
This article corresponds to "r language combat" the 9th chapter: Variance analysis; Chapter 10th: Efficacy Analysis====================================================================Variance Analysis:Regression analysis is to predict the quantified response variables by quantifying the Predictor variables, while the explanatory variables contain either nominal or ordered factor variables, the focus of our attention is usually shifted from the prediction to the analysis of the group difference,
The basic idea of topological ordering for AOV Networks is:Select a vertex output of 0 in the AoV net, then delete the vertex and remove the arc with this vertex as the tail, continue repeating this step until all vertices in the output or AOV are not present in the 0-degree vertex.AOV Network and adjacency table data structure:Code:#include "stdio.h" #include "s
MM now to the algorithm stage, more code, it is recommended to have time to knock on the computer, deepen understanding.Now, let's take the problem into:1, what is the sort of topology?Topological ordering of a forward-free graph is to arrange all the vertices in G into a linear sequence, so that any pair of vertices u and V in the graph, if the Edge (u,v) ∈e (G), the U appears before v in a linear sequence.A network should be a direction-free graph, that is, should not have a loop, because if t
1. Basic Concepts:
Ordered graphs, each vertex has a precursor and a successor relationship.
In real life, we can use a direction diagram to represent a project, the vertex table is an activity, a---------->b says: A must be preceded by activity B. This kind of graph is called the "Top expression activity network (active on vertices)"
--As a AOV network.
All vertices are sorted in a linear order sequence. The operation of the topological ordered seque
Http://acm.hdu.edu.cn/showproblem.php? PID = 1, 1285
Topological sorting: order problems
AOV network:Activities are represented by vertices, and edges represent Directed Graphs with priority relationships between activities. Directed loops should not appear in the AOV network. If a ring exists, an activity is determined by itself.
1 #include
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