ocaml: phase 5.1 stock_two.ml baseline (best of 2 transactions = 6)

Two-pass partition DP for max profit with at most 2 transactions:

  left[i]  = max single-trans profit in prices[0..i]
              (forward scan tracking running min)
  right[i] = max single-trans profit in prices[i..n-1]
              (backward scan tracking running max)
  answer   = max over i of (left[i] + right[i])

For [3; 3; 5; 0; 0; 3; 1; 4]:
  optimal partition i = 2:
    left[2]  = sell@5 after buy@3            = 2
    right[2] = sell@4 after buy@0 in [2..7]  = 4
                                       total = 6

Tests parallel forward + backward passes on parallel DP arrays,
mixed ref + array state, for downto + for ascending scans on
the same data.

190 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -166,6 +166,7 @@
   "shuffle.ml": 55,
   "simpson_int.ml": 10000,
   "stable_unique.ml": 46,
+  "stock_two.ml": 6,
   "subseq_check.ml": 3,
   "tail_factorial.ml": 479001600,
   "tarjan_scc.ml": 4,

lib/ocaml/baseline/stock_two.ml

@@ -0,0 +1,29 @@
+let max_profit_two prices =
+  let n = Array.length prices in
+  if n < 2 then 0
+  else begin
+    let left = Array.make n 0 in
+    let min_p = ref prices.(0) in
+    for i = 1 to n - 1 do
+      if prices.(i) < !min_p then min_p := prices.(i);
+      let p = prices.(i) - !min_p in
+      left.(i) <- if p > left.(i - 1) then p else left.(i - 1)
+    done;
+    let right = Array.make n 0 in
+    let max_p = ref prices.(n - 1) in
+    for i = n - 2 downto 0 do
+      if prices.(i) > !max_p then max_p := prices.(i);
+      let p = !max_p - prices.(i) in
+      right.(i) <- if p > right.(i + 1) then p else right.(i + 1)
+    done;
+    let best = ref 0 in
+    for i = 0 to n - 1 do
+      let total = left.(i) + right.(i) in
+      if total > !best then best := total
+    done;
+    !best
+  end
+
+;;
+
+max_profit_two [| 3; 3; 5; 0; 0; 3; 1; 4 |]