Module `Base.Binary_search`

General functions for performing binary searches over ordered sequences given length and get functions.

These functions can be specialized and added to a data structure using the functors supplied in Binary_searchable and described in Binary_searchable_intf.

Examples

Below we assume that the functions get, length and compare are in scope:

(* Find the index of an element [e] in [t] *)
binary_search t ~get ~length ~compare `First_equal_to e;

(* Find the index where an element [e] should be inserted *)
binary_search t ~get ~length ~compare `First_greater_than_or_equal_to e;

(* Find the index in [t] where all elements to the left are less than [e] *)
binary_search_segmented t ~get ~length ~segment_of:(fun e' ->
  if compare e' e <= 0 then `Left else `Right) `First_on_right

val binary_search : ?⁠pos:int -> ?⁠len:int -> 't -> length:('t -> int) -> get:('t -> int -> 'elt) -> compare:('elt -> 'key -> int) -> [ `Last_strictly_less_than | `Last_less_than_or_equal_to | `Last_equal_to | `First_equal_to | `First_greater_than_or_equal_to | `First_strictly_greater_than ] -> 'key -> int option

binary_search ?pos ?len t ~length ~get ~compare which elt takes t that is sorted in increasing order according to compare, where compare and elt divide t into three (possibly empty) segments:

      |  < elt  |  = elt  |  > elt  |

binary_search returns the index in t of an element on the boundary of segments as specified by which. See the diagram below next to the which variants.

By default, binary_search searches the entire t. One can supply ?pos or ?len to search a slice of t.

binary_search does not check that compare orders t, and behavior is unspecified if compare doesn't order t. Behavior is also unspecified if compare mutates t.

val binary_search_segmented : ?⁠pos:int -> ?⁠len:int -> 't -> length:('t -> int) -> get:('t -> int -> 'elt) -> segment_of:('elt -> [ `Left | `Right ]) -> [ `Last_on_left | `First_on_right ] -> int option

binary_search_segmented ?pos ?len t ~length ~get ~segment_of which takes a segment_of function that divides t into two (possibly empty) segments:

      | segment_of elt = `Left | segment_of elt = `Right |

binary_search_segmented returns the index of the element on the boundary of the segments as specified by which: `Last_on_left yields the index of the last element of the left segment, while `First_on_right yields the index of the first element of the right segment. It returns None if the segment is empty.

By default, binary_search searches the entire t. One can supply ?pos or ?len to search a slice of t.

binary_search_segmented does not check that segment_of segments t as in the diagram, and behavior is unspecified if segment_of doesn't segment t. Behavior is also unspecified if segment_of mutates t.