• CoffeeNode bSearch
  
  
  • Why?
  
  
  • bSearch.equality
  
  
  • bSearch.interval
  
  
  • bSearch.closest
  
  
  • Remarks
  
  
  • Caveats
  
  
  
  

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CoffeeNode bSearch

CoffeeNode bSearch is a binary search implementation for JavaScript; it includes equality and proximity
search methods. Say npm install coffeenode-bsearch and start searching faster today!

Why?

Binary search is a valuable tool to quickly locate items in sorted collections. Although anyone who has
ever used a dictionary or a telephone directory to locate some piece of information has naturally employed
an informal version of binary search, sadly this important algorithm is not too frequently implemented correctly;
as one writer put it,
"Nearly All Binary Searches and Mergesorts are broken" (notwithstanding, it may very well be that the
module presented here has its flaws and bugs; feel free to report issues). Assuming a correct
implementation, binary search will do at most ⌊log₂(N)+1⌋ comparisons, which means that when
you otherwise had to look at up to a million values with a linear search, you'll get away with twenty
comparisons when doing binary search.

Another reason to publish yet another module for binary search is the scarcity of turn-key solutions that
(1) incorporate the most obvious and useful generalizations of binary search, and (2) do not rely
on special data structures like balanced trees (which most of the time you'd have to build before you can
search; given that the entire motivation for doing a binary search instead of a linear search is the sheer
amount of data to be searched, this can lead to significant overhead. I'm not a particular fan of algorithms
that force you to build a non-general data structure upfront that you'll then maybe only use once before
throwing it away).

There are three methods exported by this module; in order of ascending generality (yes, you can do a
mental binary search to locate the method that best fits your use case ;-):

• 
  

  Equality Search will return the index of a data list argument that equals the
  probe search for, or null if no element matches;

  
  


• 
  

  Interval Search which will return a possibly empty list of indices with those
  elements of the data list that lie within a given distance form a certain probe; and

  
  


• 
  

  Proximity Search which will return the index of that element that lies closest
  to a given probe.

  
  

It is possible to use your own comparison functions with these methods, so distance and ordering metrics
are in no way confined to the canonical example (i.e. locating a match in an ordered list of numbers which
are tested with the <, ==, and > operators).

bSearch.equality

bSearch.equality takes a list of sorted values (in ascending order) and either a probe value or else a
comparison handler as arguments; on success, it returns the index of the probe (or the value selected by the
comparison handler) within the data or else null:

bSearch = require 'coffeenode-bsearch'
http://oeis.org/A000217: Triangular numbers

data = [ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253,
  276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946,
  990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431 ]
idx = bSearch.equality data, 300
if idx?
  # prints 24 300
  console.log idx, data[ idx ]
else
  console.log 'not found'

You can do more if you pass in a comparison handler instead of a probe value; the handler should accept
a single value (and possibly the current index) and return 0 where the probe is considered to equal the
value, -1 when the probe is less than the value, and +1 otherwise. This is exemplified by the default
handler used internally by bSearch.equality:

handler = ( value, idx ) =>
  return  0 if probe == value
  return -1 if probe <  value
  return +1

bSearch.interval

bSearch.interval builds on bSearch.equality, but instead of returning a single index, it tries to find
a contiguous range of matching indices. With the same data as in the previous example:

probe = 300
delta = 100
compare = ( value ) ->
  return  0 if probe - delta <= value <= probe + delta
  return -1 if probe - delta < value
  return +1
[ lo_idx, hi_idx ] = bSearch.interval data, compare
if lo_idx?
  # prints [ 20, 27 ] [ 210, 378 ]
  console.log [ lo_idx, hi_idx, ], [ data[ lo_idx ], data[ hi_idx ], ]
else
  console.log 'not found'

The printout tells us that values between 200 and 400 are to be found in positions 20 thru 27 of the
given data.

bSearch.closest

bSearch.closest works like bSearch.equality, except that it always returns a non-null index for a
non-empty data list, and that the result will point to (one of) the closest neighbors to the probe or
distance function passed in. With the same data as in the previous examples:

handler = ( value, idx ) =>
  return probe - value
probe = 1000
idx   = BS.closest data, probe
if idx?
  # prints 44 990
  console.log idx, data[ idx ]
else
  console.log 'not found'

The second argument to bSearch.closest may be a distance function similar to the one shown here or else
a probe value; in the latter case, the default distance function shown above will be used.

Remarks

• When the data argument is not sorted in a way that is compliant with the ordering semantics of the
  implicit or explicit comparison handler, the behavior of both methods is undefined.

With 'ordering semantics' we here simple mean that when run across the entire data list, the values
d_i returned by the comparison function must always obey
d_i <= d_j when i <= j.
As such, you can have a data list of numerically descending values
as long as your handler returns a series of non-descending comparison metrics when iterating over the list.

• 
  

  When you use a comparison handler that returns 0 for a range of values with the bSearch.equality
  method, the returned index, if any, may point to any 'random' matching value; without knowing the data (and
  the search algorithm), there is no telling which list element will be picked out.

  
  


• 
  

  Likewise, when using a distance function that returns the same minimum distance for more than a single
  value with the bSearch.closest method, the returned index, if any, may point to any 'random' matching
  value.

  
  


• 
  

  Be aware that bSearch always uses JavaScript's strict
  equality operator unless you pass in a comparison function. Strict equality comparisons
  have their limitations and are generally
  not to be used when comparing anything but numbers or else texts that are sorted according to Unicode
  character values.

  
  

Caveats

This module has no test suite as yet, so its correctness and performance are more of a conjecture than a
proven fact. Also, we do presently no memoizing of comparison results which may or may not lead to
sub-optimal performance; since the implementation is intended to be completely agnostic as for the nature
of the searched data, caching is hardly to be implemented easily and correctly for the general case.

If indeed your comparison (or distance) function does rely on lengthy calculations, consider to implement
a memoizing functionality that fits your use case.