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Module:Exponential search

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Warning This Lua module is used on approximately 715,000 pages, or roughly 1% of all pages .
To avoid major disruption and server load, any changes should be tested in the module's /sandbox or /testcases subpages, or in your own module sandbox. The tested changes can be added to this page in a single edit. Consider discussing changes on the talk page before implementing them.

This module provides a generic exponential search algorithm. This kind of search can be useful when you want to find a key in some kind of sorted array, and you want to do it by checking as few array elements as possible. This could include situations like:

  • Finding the highest archive number in a set of archives without checking whether they all exist.
  • Finding the number of positional arguments in frame.args without having to expand the wikitext for each of them.

You shouldn't use this module if any of the following apply:

  1. You can use the Lua length operator to find what you need.
  2. Your array has any gaps in it. (In other words, any of the items before the final item is nil, e.g. {'foo','bar',nil,'baz'}.) If you try and use this module on a sparse array, you might get an erroneous value.
  3. Your array has fewer than about 10 items. It's possible to use this module for those arrays, but you will access most of the array elements anyway (perhaps some of them twice), and your code will be more complicated than if you just used a for loop.

Usage

First, load the module. 

localexpSearch=require('Module:Exponential search')

You can then use the expSearch function with the following syntax: 

expSearch(testFunc,init)

Parameters:

  • testFunc - a test function for your array. This function should take a positive integer i as its first parameter. If the element corresponding to i is not in the array, then the function should return false or nil; and if it is in the array, then the function should return a truthy value (anything other than false or nil). (required)
  • init - the initial value of i to check. For advanced users. (optional)

expSearch will return the highest value of i for which testFunc was truthy. If no values were truthy, the function will return nil.

Examples

Jimbo's talk archives

User talk:Jimbo Wales has archives at User talk:Jimbo Wales/Archive 1, User talk:Jimbo Wales/Archive 2, ... To find the highest archive number, you would use code like this: 

localexpSearch=require('Module:Exponential search')
localhighestArchive=expSearch(function(i)
localarchive='User talk:Jimbo Wales/Archive '..i
returnmw.title.new(archive).exists
end)

Village pump archives

Wikipedia:Village pump (proposals) has old archives at Wikipedia:Village pump (proposals)/Archive A, Wikipedia:Village pump (proposals)/Archive B, etc. After they go through to Archive Z, the next archive is Archive AA. Although these archives aren't being updated anymore, as a demonstration we can find the highest one using this module; all we need is a function that converts from an integer to the corresponding archive name. 

localexpSearch=require('Module:Exponential search')
localfunctionintegerToAlpha(i)
-- This function converts 1 to A, 2 to B, ... 26 to Z, 27 to AA, ...
localret=''
whilei>0do
localrem=i%26
ifrem==0then
rem=26
end
localchar=string.char(rem+64)-- the "rem"th letter of the alphabet
ret=char..ret
i=(i-rem)/26
end
returnret
end
localfunctionintegerToArchive(i)
return'Wikipedia:Village pump (proposals)/Archive '..integerToAlpha(i)
end
localhighestInteger=expSearch(function(i)
localarchive=integerToArchive(i)
returnmw.title.new(archive).exists
end)
localhighestArchive=integerToArchive(highestInteger)
The above documentation is transcluded from Module:Exponential search/doc. (edit | history)
Editors can experiment in this module's sandbox (create | mirror) and testcases (edit | run) pages.
Subpages of this module.

 -- This module provides a generic exponential search algorithm.
 require[[strict]]

 localcheckType=require('libraryUtil').checkType
 localfloor=math.floor

 localfunctionmidPoint(lower,upper)
 returnfloor(lower+(upper-lower)/2)
 end

 localfunctionsearch(testFunc,i,lower,upper)
 iftestFunc(i)then
 ifi+1==upperthen
 returni
 end
 lower=i
 ifupperthen
 i=midPoint(lower,upper)
 else
 i=i*2
 end
 returnsearch(testFunc,i,lower,upper)
 else
 upper=i
 i=midPoint(lower,upper)
 returnsearch(testFunc,i,lower,upper)
 end
 end

 returnfunction(testFunc,init)
 checkType('Exponential search',1,testFunc,'function')
 checkType('Exponential search',2,init,'number',true)
 ifinitand(init<1orinit~=floor(init)orinit==math.huge)then
 error(string.format(
 "invalid init value '%s' detected in argument #2 to "..
 "'Exponential search' (init value must be a positive integer)",
 tostring(init)
 ),2)
 end
 init=initor2
 ifnottestFunc(1)then
 returnnil
 end
 returnsearch(testFunc,init,1,nil)
 end

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