C programming fill in the following code #include "graph.h" #include #include /* initialise an empty graph */ /* return pointer to initialised graph */ Graph *init_graph(void) { } /* release memory for graph */ void free_graph(Graph *graph) { } /* initialise a vertex */ /* return pointer to initialised vertex */ Vertex *init_vertex(int id) { } /* release memory for initialised vertex */ void free_vertex(Vertex *vertex) { } /* initialise an edge. */ /* return pointer to initialised edge. */ Edge *init_edge(void) { } /* release memory for initialised edge. */ void free_edge(Edge *edge) { } /* remove all edges from vertex with id from to vertex with id to from graph. */ void remove_edge(Graph *graph, int from, int to) { } /* remove all edges from vertex with specified id. */ void remove_edges(Graph *graph, int id) { } /* output all vertices and edges in graph. */ /* each vertex in the graphs should be printed on a new line */ /* each vertex should be printed in the following format: */ /* vertex_id: edge_to_vertex[weight] edge_to_vertex[weight] ... */ /* for example: */ /* 1: 3[1.00] 5[2.00] */ /* indicating that vertex id 1 has edges to vertices 3 and 5 */ /* with weights 1.00 and 2.00 respectively */ /* weights should be output to two decimal places */ void print_graph(Graph *graph) { } /* find vertex with specified id in graph. */ /* return pointer to vertex, or NULL if no vertex found. */ Vertex *find_vertex(Graph *graph, int id) { } /* create and add vertex with specified id to graph. */ /* return pointer to vertex or NULL if an error occurs. */ /* if vertex with id already exists, return pointer to existing vertex. */ Vertex *add_vertex(Graph *graph, int id) { } /* remove vertex with specified id from graph. */ /* remove all edges between specified vertex and any other vertices in graph. */ void remove_vertex(Graph *graph, int id) { } /* add directed edge with specified weight between vertex with id from */ /* to vertex with id to. */ /* if no vertices with specified ids (from or to) exist */ /* then the vertices will be created. */ /* multiple edges between the same pair of vertices are allowed. */ /* return pointer to edge, or NULL if an error occurs found. */ Edge *add_edge(Graph *graph, int from, int to, double weight) { } /* add two edges to graph, one from vertex with id from to vertex with id to, */ /* and one from vertex with id to to vertex with id from. */ /* both edges should have the same weight */ /* if no vertices with specified ids (from or to) exist */ /* then the vertices will be created. */ /* multiple vertices between the same pair of vertices are allowed. */ void add_edge_undirected(Graph *graph, int from, int to, double weight) { } /* return array of node ids in graph. */ /* array of node ids should be dynamically allocated */ /* set count to be the number of nodes in graph */ /* return NULL if no vertices in graph */ int *get_vertices(Graph *graph, int *count) { } /* return array of pointers to edges for a given vertex. */ /* array of edges should be dynamically allocated */ /* set count to be number of edges of vertex */ /* return NULL if no edges from/to vertex */ Edge **get_edges(Graph *graph, Vertex *vertex, int *count) { } /* return pointer to edge from vertex with id from, to vertex with id to. */ /* return NULL if no edge */ Edge *get_edge(Graph *graph, int from, int to) { } /* return id of destination node of edge. */ int edge_destination(Edge *edge) { } /* return weight of edge. */ double edge_weight(Edge *edge) { }