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Largest BST subtree in a given Binary Tree
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| open Core.Std | |
| type tree = Empty | Node of int * tree * tree | |
| let rec largest_bst t = | |
| let min_exn (lst:int list) : int = | |
| Option.value_exn (List.min_elt lst ~cmp:Int.compare) | |
| and max_exn (lst:int list) : int = | |
| Option.value_exn (List.max_elt lst ~cmp:Int.compare) | |
| in | |
| match t with | |
| | Empty -> (true, 0, Empty, Int.max_value, Int.min_value) | |
| | Node (v, l, r) -> | |
| let (top_r, size_r, lar_r, rmin, rmax) = largest_bst r in | |
| let (top_l, size_l, lar_l, lmin, lmax) = largest_bst l in | |
| let new_min = min_exn [lmin; rmin; v] in | |
| let new_max = max_exn [rmax; lmax; v] in | |
| let valid_left = (l = Empty) || (lmin < v && lmax < v) in | |
| let valid_right = (r = Empty) || (rmin > v && rmax > v) in | |
| match (top_l, top_r) with | |
| | (true, true) when valid_right && valid_left -> | |
| (true, size_l + size_r + 1, t, new_min, new_max) | |
| | _ -> | |
| if size_l > size_r then | |
| (false, size_l, lar_l, new_min, new_max) | |
| else | |
| (false, size_r, lar_r, new_min, new_max) | |
| let () = | |
| let t1 = Node (5, Node (2, Node (1, Empty, Empty), | |
| Node (3, Empty, Empty)), | |
| Node (4, Empty, Empty)) in | |
| let t2 = Node (50, Node (10, Node (5, Empty, Empty), Node (20, Empty, Empty)), | |
| Node (60, Node (55, Node (45, Empty, Empty), Empty), | |
| Node (70, Node (65, Empty, Empty), | |
| Node (80, Empty, Empty)))) in | |
| let t3 = Node (50, Node (30, Node (5, Empty, Empty), Node (20, Empty, Empty)), | |
| Node (60, Node (45, Empty, Empty), | |
| Node (70, Node (65, Empty, Empty), | |
| Node (80, Empty, Empty)))) in | |
| let (_, s1, _, _, _) = largest_bst t1 in | |
| let (_, s2, _, _, _) = largest_bst t2 in | |
| let (_, s3, _, _, _) = largest_bst t3 in | |
| printf "%d\n%d\n%d\n" s1 s2 s3 |
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