Data Structure: Graph -- topological sorting

Data Structure: Graph -- topological sorting

Topological sorting

Topological sorting

In practical application, the edges of a directed graph can be seen as the constraints between vertices. When we regard a vertex as a task It indicates that task Vj must be completed after task Vi is completed, that is, task Vi is completed before task Vj. For a directed graph, find a vertex sequence and the sequence is satisfied: If the vertex Vi and Vj have an edge In this sequence, vertex Vi must be before vertex Vj. Such a sequence is called the topological sequence of a directed graph (topological order ).

Procedure

 

Select a vertex output without a forward (with an inbound degree of 0) from the directed graph. Delete all the arcs starting with it in the graph. Repeat the preceding two steps. There are two situations: 1. All vertices have been output, and the output sequence is the topological sequence. 2. There are no vertices without a precursor, but any vertex has no output, which indicates that the directed graph has a ring. It can be seen that topological sorting can detect whether a directed graph has loops. It must be noted that, even if the storage structure is determined, the topological sequence is not necessarily unique. The topological sorting sequence is related not only to the storage structure but also to the specific algorithm used.
Code Class Definition

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Using namespace std;/* Graph Topology Sorting using the adjacent matrix must be directed Graph */class Graph {private: // Number of vertices int numV; // Number of edges int numE; // vertex input int * indegree; // The adjacent matrix int ** matrix; public:/* constructor numV indicates the number of vertices, and whether isWeighted has a weight, whether isDirected has a direction */Graph (int numV); // create a Graph void createGraph (int numE); // The Destructor ~ Graph (); // get the number of vertices int getVerNums () {return numV;} // get the number of edges int getEdgeNums () {return numE ;} // Topology Sorting void topologicalSort (); // print the adjacent matrix void printAdjacentMatrix (); // check the input bool check (int, int );};
   
  
 

Class implementation

// Constructor, specify the number of vertices Graph: Graph (int numV) {// checks the number of input vertices while (numV <= 0) {cout <incorrect number of vertices! Re-input; cin> numV;} this-> numV = numV; // construct the adjacent matrix and initialize matrix = new int * [numV]; int I, j; for (I = 0; I <numV; I ++) matrix [I] = new int [numV]; // because the weights have no effect on topological sorting, therefore, the unauthorized graph is used for (I = 0; I <numV; I ++) for (j = 0; j <numV; j ++) matrix [I] [j] = 0; // construct the vertex's inbound array and initialize indegree = new int [numV]; for (I = 0; I <numV; I ++) indegree [I] = 0;} void Graph: createGraph (int numE) {/* checks the number of input edges for a directed Graph of numV vertices, up to numV * (numV-1) edges */while (NumE <0 | numE> numV * (numV-1) {cout <The number of sides is incorrect! Re-input; cin> numE;} this-> numE = numE; int tail, head, I; I = 0; cout <enter the start point of each edge (arc tail), endpoint (ARC header) <endl; while (I <numE) {cin> tail> head; while (! Check (tail, head) {cout <the input edge is incorrect! Enter <endl; cin> tail> head;} matrix [tail] [head] = 1; indegree [head] ++; I ++;} again ;}} graph ::~ Graph () {int I; for (I = 0; I <numV; I ++) delete [] matrix [I]; delete [] matrix; delete [] indegree ;} // Topology Sorting void Graph: topologicalSort () {int I, vertex; queue
 
  
Q; // for (I = 0; I <numV; I ++) if (indegree [I] = 0) q. push (I); bool * visited = new bool [numV]; for (I = 0; I <numV; I ++) visited [I] = false; while (! Q. empty () {vertex = q. front (); q. pop (); cout <setw (4) <vertex; visited [vertex] = true; for (I = 0; I <numV; I ++) if (matrix [vertex] [I] = 1) {// adjust the inbound level. if the inbound level is 0, you need to join if (! (-- Indegree [I]) q. push (I) ;}} cout <endl; for (I = 0; I <numV; I ++) if (! Visited [I]) cout <This directed graph has a ring !; Cout <endl; delete [] visited;} // print the adjacent matrix void Graph: printAdjacentMatrix () {int I, j; cout. setf (ios: left); cout <setw (4) <; for (I = 0; I <numV; I ++) cout <setw (4) <I; cout <endl; for (I = 0; I <numV; I ++) {cout <setw (4) <I; for (j = 0; j <numV; j ++) cout <setw (4) <matrix [I] [j]; cout <endl ;}} bool Graph: check (int tail, int head) {if (tail <0 | tail> = numV | head <0 | head> = numV) return false; return true ;}
 

Main Function

Int main () {cout <******* topological sorting ***** by David ***** <endl; int numV, numE; cout <graph creation... <endl; cout <number of input vertices; cin> numV; Graph graph (numV); cout <number of input edges; cin> numE; graph. createGraph (numE); cout <print the adjacent matrix... <endl; graph. printAdjacentMatrix (); cout <topological sorting... <
 
  
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