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.
Below we assume that the function 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_rightval 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 optionbinary_search ?pos ?len t ~length ~get ~compare which elt takes t that is sorted
in nondecreasing 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 optionbinary_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.