assignment

assignment/digraph.ml

@@ -0,0 +1,98 @@
+module VertexMap = Map.Make(String)
+
+type t = ((string * int) list) VertexMap.t
+type edge = string * string * int
+
+exception Invalid of string
+
+(** [empty] is the empty digraph. *)
+let empty = VertexMap.empty
+
+(** [validate_edge (v1, v2, ed_len)] checks whether an edge is valid.
+  * It raises [Invalid] if either vertex is empty, if the vertices
+  * are the same, or if the edge length is not positive.
+  *)
+let validate_edge ((v1, v2, ed_len) : edge) : unit =
+  if v1 = "" then
+    raise (Invalid "source vertex cannot be empty")
+  else if v2 = "" then
+    raise (Invalid "destination vertex cannot be empty")
+  else if v1 = v2 then
+    raise (Invalid "source and destination must be distinct")
+  else if ed_len <= 0 then
+    raise (Invalid "edge length must be positive")
+  else
+    ()
+
+(** [add_edge (v1, v2, ed_len) graph] returns a new graph with the given
+  * directed edge added.
+  * It raises [Invalid] if the edge is invalid or if an edge with the
+  * same source and destination already exists.
+  *)
+let add_edge ((v1, v2, ed_len) : edge) (graph : t) : t =
+  let _ = validate_edge (v1, v2, ed_len) in
+  let existing_edges =
+    match VertexMap.find_opt v1 graph with
+    | Some edges -> edges
+    | None -> []
+  in
+  if List.exists (fun (dest, _) -> dest = v2) existing_edges then
+    raise (Invalid "duplicate edge")
+  else
+    VertexMap.add v1 ((v2, ed_len) :: existing_edges) graph
+
+(** [of_edges ls] builds a digraph from the list of edges [ls].
+  * It raises [Invalid] if any edge in [ls] is invalid or duplicated.
+  *)
+let of_edges (ls : edge list) : t =
+  List.fold_left (fun acc edge -> add_edge edge acc) empty ls
+
+(** [edges graph] returns a sorted list of all distinct edges in [graph].
+  * The edges are sorted first by source vertex, then by destination vertex.
+  *)
+let edges (graph : t) : edge list =
+  let compare_edges (v1, v2, _) (va, vb, _) =
+    let cmp1 = String.compare v1 va in
+    if cmp1 <> 0 then
+      cmp1
+    else
+      String.compare v2 vb
+  in
+  let all_edges =
+    VertexMap.fold
+      (fun src neighbors acc ->
+        List.fold_left
+          (fun inner_acc (dest, len) -> (src, dest, len) :: inner_acc)
+          acc
+          neighbors)
+      graph
+      []
+  in
+  List.sort compare_edges all_edges
+
+(** [vertices graph] returns a sorted list of all distinct vertices
+  * in [graph].
+  * This includes vertices that appear only as destinations.
+  *)
+let vertices (graph : t) : string list =
+  let vertex_list =
+    VertexMap.fold
+      (fun src neighbors acc ->
+        let acc_with_src = src :: acc in
+        List.fold_left
+          (fun inner_acc (dest, _) -> dest :: inner_acc)
+          acc_with_src
+          neighbors)
+      graph
+      []
+  in
+  List.sort_uniq String.compare vertex_list
+
+(** [neighbors vtx graph] returns the outgoing neighbors of [vtx]
+  * as a list of [(destination, length)] pairs.
+  * If [vtx] has no outgoing edges, it returns the empty list.
+  *)
+let neighbors vtx (graph : t) : (string * int) list =
+  match VertexMap.find_opt vtx graph with
+  | Some verts -> verts
+  | None -> []