19 Grafos 1

GRAFOS ESTRUCTURA DE DATOS www.espol.edu.ec www.fiec.espol.edu.ec

INTRODUCCION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Dado un escenario donde ciertos objetos se relacionan, se puede “modela el grafo” y luego aplicar algoritmos para resolver diversos problemas Impresora Modem PC2 Servidor PC1

DEFINICION ,[object Object],[object Object],[object Object],[object Object],[object Object],V = {1, 4, 5, 7, 9} A= {(1,4), (4,9), (9,7), (7,5), (5,1), (4,1), (1,5), (5,7), (7, 9), (9,4)} 1 4 5 7 9

TIPOS DE GRAFOS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],V = {C, D, E, F, H} A= {(E,H), (H,E), (E,C), (C,D), (D,F)} Grafo del ejemplo anterior C E D F H 1 4 5 7 9

OTROS CONCEPTOS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Guayaquil Quito Cuenca Ambato Riobamba 5 5 7 9 8 7

GRADOS DE UN NODO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Gradoent(D) = 1 y Gradsal(D) = 1 Grado(Guayaquil) = 3 C E D F H Guayaquil Quito Cuenca Ambato Riobamba 5 5 7 9 8 7

CAMINOS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Camino entre 4 y 7 P = {4, 6, 9, 7} Longitud: 3 Camino A y A P = {A, E, B, F, A} Longitud: 4 – 4ciclo 4 7 9 6 10 11 A B C D E F

CONECTIVIDAD ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],3 9 5 7 2 4 5 6 8 H A B D

TDA GRAFO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

REPRESENTACION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

MATRIZ DE ADYACENCIA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Si el grafo fuese valorado, en vez de 1, se coloca el factor de peso 4 7 9 6 10 11 V 0 V 1 V 2 V 3 V 4 V 5

EL TIPO DE DATO ,[object Object],[object Object],[object Object],[object Object],#define MAX 20 typedef int [MAX][MAX] MatrizAdy; typdef Generico[MAX] GRAPH_Vertex ; typedef struct GRAPH { GRAPH_Vertex V; MatrizAdy A; int nvertices; bool Dirigido; };

UNIR VERTICE void Union(GRAPH G, int v1, int v2){ G->A[v1][v2] = 1; if(!G->dirigido) G->A[v2][v1] = 1; }

LISTA DE ADYACENCIA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],4 7 9 6 10 11 4 6 9 7 10 11 6 4 6 9 11 10 9 7

EL TIPO DE DATO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],struct GRAPH_Vertex { //Vértice Generic info; List *lst_adj; Mark visit; }; struct GRAPH_Edge //Arco { int weight; GRAPH_Vertex *destination; GRAPH_Vertex *origin; }; typedef struct { //Grafo List LVertices; bool dirigido; } GRAPH ;

ALGUNAS IMPLEMENTACIONES void Union( GRAPH G, GRAPH_Vertex V1, GRAPH_Vertex V2, int peso){ GRAPH_Edge *arc; arc = GRAPH_Edge_New(G,V1,V2,peso); if (arc) { List_InsertAfterLast (V1->lst_adj,NodeList_New(arc)); if(!G->dirigido) List_InsertAfterLast (V2->lst_adj, NodeList_New(arc)); } }

EJERCICIO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

RECORRIDOS DEL GRAFO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

RECORRIDO EN ANCHURA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

EJEMPLO A T H B D C R D Cola Se Muestra: D B C B C C H H R H R A R A T T A T T

IMPLEMENTACION ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

RECORRIDO EN PROFUNDIDAD ,[object Object],[object Object],[object Object],[object Object],[object Object],A T H B D C R Se Muestra: Pila D D B C C R R H H A T T A B

EJERCICIO Escriba la implementación del recorrido en profundidad de un grafo a partir de un vértice inicial

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