ocaml: phase 5.1 bipartite.ml baseline (7-node bipartite, 4 in color 0)

BFS-based 2-coloring of an undirected graph:

  edges (undirected):
    0-1  0-3  1-2  1-4  2-5  3-4  3-6  5-6

  Partition: {0, 2, 4, 6} vs {1, 3, 5} (no odd cycles)

Returns count of color-0 vertices (4) on success, -1 on odd-cycle
detection.

Tests Queue-based BFS with a source-loop wrapper for disconnected
graphs, `1 - color.(u)` toggle, color-equality conflict check
on already-colored neighbors.

164 baseline programs total.

lib/ocaml/baseline/bipartite.ml

@@ -0,0 +1,39 @@
+let is_bipartite n adj =
+  let color = Array.make n (-1) in
+  let ok = ref true in
+  let q = Queue.create () in
+  for src = 0 to n - 1 do
+    if color.(src) = -1 then begin
+      color.(src) <- 0;
+      Queue.push src q;
+      while not (Queue.is_empty q) do
+        let u = Queue.pop q in
+        List.iter (fun v ->
+          if color.(v) = -1 then begin
+            color.(v) <- 1 - color.(u);
+            Queue.push v q
+          end else if color.(v) = color.(u) then
+            ok := false
+        ) adj.(u)
+      done
+    end
+  done;
+  let zeros = ref 0 in
+  for i = 0 to n - 1 do
+    if color.(i) = 0 then zeros := !zeros + 1
+  done;
+  if !ok then !zeros else -1
+
+;;
+
+let n = 7 in
+let adj = [|
+  [1; 3];
+  [0; 2; 4];
+  [1; 5];
+  [0; 4; 6];
+  [1; 3];
+  [2; 6];
+  [3; 5]
+|] in
+is_bipartite n adj

lib/ocaml/baseline/expected.json

@@ -12,6 +12,7 @@
   "bisect.ml": 141,
   "bigint_add.ml": 28,
   "binary_heap.ml": 123456789,
+  "bipartite.ml": 4,
   "bits.ml": 21,
   "balance.ml": 3,
   "base_n.ml": 17,