# Interpolating Search

When searching for a value in a sorted array, the to preferring search algorithm is the binary search. In certain cases although we can be a lot faster using an interpolating search mechanism. tables optimal for a interpolating search are { 1,2,3,4,5,6,7,8,9,10 }, where as tables looking like { 1,1,1,1,1,1,1,1,1,2,10 } and searching it for the value 2 will use a alot more time than the binary search. So it depends on the scenario, but if used right one can be 3 times as fast as the binary search. I wrote an extra function for searching a reversed table, since it was the better option rather to changing all the variables and the < check.

```--[[
Interpolating Search v 0.2

LUA 5.1 compatible

Can only search for values of type number

table.intsearch( table, value [, compval ] ), for searching a normal sorted table
table.intsearchrev( table, value [, compval ] ), for searching a reversed sorted table

If the  value is found:
it returns a table holding all the matching indices (e.g. { startindice,endindice } )
endindice may be the same as startindice if only one matching indice was found
If compval is given:
then it must be a function that takes one value and returns a second value2,
to be compared with the searched value, e.g.:
compvalue = function( value ) return value[1] end
Return value:
on success: a table holding matching indices (e.g. { startindice,endindice } )
on failure: nil
]]--
do
-- Avoid heap allocs for performance
local default_fcompval = function( value ) return value end
function table.intsearch( t,value,fcompval )
-- Initialise functions
local fcompval = fcompval or default_fcompval
-- Inistialise numbers
local ilow,ihigh = 1,#t
-- return on empty table
if not t[ilow] then return end
-- get values of indices
local _ilow,_ihigh = fcompval( t[ilow] ),fcompval( t[ihigh] )
-- make sure slope cannot become 0
while _ilow and _ilow < _ihigh do
-- get interpolated position
local pos = math.floor( (value-_ilow)*(ihigh-ilow)/(_ihigh-_ilow) ) + ilow
-- check for out of range
if pos < ilow or pos > ihigh then return end
-- get compare value
local compval = fcompval( t[pos] )
if value == compval then
-- insert found position
local tfound,num = { pos,pos },pos-1
-- get all values that match
while value == fcompval( t[num] ) do
tfound[1],num = num,num-1
end
num = pos+1
while value == fcompval( t[num] ) do
tfound[2],num = num,num+1
end
return tfound
-- keep searching,
-- left part of the table
elseif value < compval then
ihigh = pos-1
else
ilow = pos+1
end
_ilow,_ihigh = fcompval( t[ilow] ),fcompval( t[ihigh] )
end
if value == fcompval( t[ilow] ) then
-- only add values --> of ilow
local tfound,num = { ilow,ilow },ilow+1
while value == fcompval( t[num] ) do
tfound[2],num = num,num+1
end
return tfound
end
end
-- Interpolated search on a reversed table
function table.intsearchrev( t,value,fcompval )
-- Initialise functions
local fcompval = fcompval or default_fcompval
-- Inistialise numbers
local ilow,ihigh = 1,#t
if not t[ilow] then return end
local _ilow,_ihigh = fcompval( t[ilow] ),fcompval( t[ihigh] )
while _ilow and _ilow > _ihigh do
-- get interpolated position
local pos = math.floor( (_ihigh-value)*(ihigh-ilow)/(_ihigh-_ilow) ) + ilow
-- check for out of range
if pos < ilow or pos > ihigh then return end
local compval = fcompval( t[pos] )
if value == compval then
-- insert found position
local tfound,num = { pos,pos },pos-1
-- get all values that match
while value == fcompval( t[num] ) do
tfound[1],num = num,num-1
end
num = pos+1
while value == fcompval( t[num] ) do
tfound[2],num = num,num+1
end
return tfound
-- keep searching,
-- left part of the table
elseif value > compval then
ihigh = pos-1
else
ilow = pos+1
end
_ilow,_ihigh = fcompval( t[ilow] ),fcompval( t[ihigh] )
end
if value == fcompval( t[ilow] ) then
-- only add values --> of ilow
local tfound,num = { ilow,ilow },ilow+1
while value == fcompval( t[num] ) do
tfound[2],num = num,num+1
end
return tfound
end
end
end
-- CHILLCODE™
```
Testsuit:
```-- test: table size 0
t = {}
local v = table.intsearch(t, 5); assert(v == nil)

-- test: table size 1
t = {5}
local v = table.intsearch(t, 4); assert(v == nil)
local v = table.intsearch(t, 5); assert(v[1] == 1)
local v = table.intsearch(t, 6); assert(v == nil)

-- test: table size 2
t = {4,6}
local v = table.intsearch(t, 3); assert(v == nil)
local v = table.intsearch(t, 4); assert(v[1] == 1)
local v = table.intsearch(t, 5); assert(v == nil)
local v = table.intsearch(t, 6); assert(v[1] == 2)
local v = table.intsearch(t, 7); assert(v == nil)

-- test: typical, with duplicate
t = {0,2,4,4,6,8,10}
local v = table.intsearch(t, 0); assert(v[1] == 1)
local v = table.intsearch(t, 10); assert(v[1] == 7)
local v = table.intsearch(t, 4); assert(v[1] == 3 and v[2] == 4)
local v = table.intsearch(t, 5); assert(v == nil)
local v = table.intsearch(t, 11); assert(v == nil)
local v = table.intsearch(t, -1); assert(v == nil)

-- test: identical
t = {1,1,1,1,1,1,1,1,1,1}
local v = table.intsearch(t, 1); assert(v[1] == 1 and v[2] == 10)

-- test: fcomp
t = {10,52,34,44,86,38}
local v = table.intsearch(t, 6, function(v) return v % 10 end); assert(v[1] == 5)
local v = table.intsearch(t, 4, function(v) return v % 10 end); assert(v[1] == 3 and v[2] == 4)

-- test: reverse
t = {10,8,6,4,4,2,0}
local v = table.intsearchrev(t, 6); assert(v[1] == 3)
local v = table.intsearchrev(t, 4); assert(v[1] == 4 and v[2] == 5)

print "DONE"
```

### Interpolating Search for a String

This combines the interpolating search with the binary search to be able to search tables holding strings. This was more a test if it is actually possible, and in some cases, this method could be faster than the binary search.

```--[[
Interpolating Search on a String

LUA 5.1 compatible

Can only search sorted tables with value string

table.intsearchstr( table, value ), for searching a normal sorted table
table.intsearchstrrev( table, value ), for searching a reversed sorted table

If the  value is found:
it returns a table holding all the matching indices (e.g. { startindice,endindice } )
endindice may be the same as startindice if only one matching indice was found
Return value:
on success: a table holding matching indices (e.g. { startindice,endindice } )
on failure: nil
]]--
do
-- Avoid heap allocs for performance
local getbytevalue = function( value )
if value then
local num,mul = 0,1
-- set bytedept, 4 or 5 seems appropriate
for i = 4,1,-1 do
local byte = string.byte( string.sub( value,i,i ) ) or -1
byte,num,mul = byte + 1,num + mul*byte,mul*257
end
return num
end
end
-- Load the optimised binary function
-- Avoid heap allocs for performance
local fcompf = function( a,b ) return a < b end
local fcompr = function( a,b ) return a > b end
local function tablebinsearch( t,value,reversed,iStart,iEnd )
-- Initialise functions
local fcomp = reversed and fcompr or fcompf
--  Initialise numbers
local iStart,iEnd,iMid = iStart or 1,iEnd or #t,0
-- Binary Search
while iStart <= iEnd do
-- calculate middle
iMid = math.floor( (iStart+iEnd)/2 )
-- get compare value
local value2 = t[iMid]
-- get all values that match
if value == value2 then
local tfound,num = { iMid,iMid },iMid - 1
while value == t[num] do
tfound[1],num = num,num - 1
end
num = iMid + 1
while value == t[num] do
tfound[2],num = num,num + 1
end
return tfound
-- keep searching
elseif fcomp( value,value2 ) then
iEnd = iMid - 1
else
iStart = iMid + 1
end
end
end

-- The interpolationg Search Function on a String
function table.intsearchstr( t,value )
-- Inistialise numbers
local ilow,ihigh = 1,#t
-- return on empty table
if not t[ilow] then return end
-- get byte values values of indices and searched value
local _ilow,_ihigh,_value = getbytevalue(t[ilow]),getbytevalue(t[ihigh]),getbytevalue(value)
local oldpos = -1
-- make sure slope cannot become 0
while _ilow and _ilow < _ihigh do
-- get interpolated position
local pos = math.floor( (_value-_ilow)*(ihigh-ilow)/(_ihigh-_ilow) ) + ilow
-- check for out of range
if pos < ilow or pos > ihigh then return end
-- check for real match
if value == t[pos] then
-- insert found position
local tfound,num = { pos,pos },pos-1
-- get all values that match
while value == t[num] do
tfound[1],num = num,num-1
end
num = pos+1
while value == t[num] do
tfound[2],num = num,num+1
end
return tfound
-- keep searching,
-- left part of the table,check for real lower
elseif value < t[pos] then
ihigh = pos-1
else
ilow = pos+1
end
-- check if new position is further than 1 away
if oldpos+1 == pos or oldpos-1 == pos then
-- start binary search
return tablebinsearch( t,value,_,ilow,ihigh )
end
_ilow,_ihigh,oldpos = getbytevalue(t[ilow]),getbytevalue(t[ihigh]),pos
end
-- initiate binary seach function here since we could be in a flat for the interpolating search
return tablebinsearch( t,value,_,ilow,ihigh )
end
-- The interpolationg Search Function on a String
function table.intsearchstrrev( t,value )
-- Inistialise numbers
local ilow,ihigh = 1,#t
-- return on empty table
if not t[ilow] then return end
-- get byte values values of indices and searched value
local _ilow,_ihigh,_value = getbytevalue(t[ilow]),getbytevalue(t[ihigh]),getbytevalue(value)
local oldpos = -1
-- make sure slope cannot become 0
while _ilow and _ilow > _ihigh do
-- get interpolated position
local pos = math.floor( (_ihigh-_value)*(ihigh-ilow)/(_ihigh-_ilow) ) + ilow
-- check for out of range
if pos < ilow or pos > ihigh then return end
-- check for real match
if value == t[pos] then
-- insert found position
local tfound,num = { pos,pos },pos-1
-- get all values that match
while value == t[num] do
tfound[1],num = num,num-1
end
num = pos+1
while value == t[num] do
tfound[2],num = num,num+1
end
return tfound
-- keep searching,
-- left part of the table,check for real lower
elseif value > t[pos] then
ihigh = pos-1
else
ilow = pos+1
end
-- check if new position is further than 1 away
if oldpos+1 == pos or oldpos-1 == pos then
-- start binary search
return tablebinsearch( t,value,1,ilow,ihigh )
end
_ilow,_ihigh,oldpos = getbytevalue(t[ilow]),getbytevalue(t[ihigh]),pos
end
-- initiate binary seach function here since we could be in a flat for the interpolating search
return tablebinsearch( t,value,1,ilow,ihigh )
end
end
-- CHILLCODE™
```
Test suit:
```-- test: table size 0
t = { "a","a","a","a","a","a","a","a","a","a","aa","z" }
local v = table.intsearchstr(t, "aa"); assert(v[1] == 11)

-- test flat for interpolatin search function
t = { "aabb","aabbcc","aabc","aabc","aabc","aabc","aabc","aabc","aabc","aabc","aabc","aabc","aabc","aabca","aabcc" }
local v = table.intsearchstr(t, "aabca"); assert(v[1] == 14)

-- test: table size 1
t = { "a" }
local v = table.intsearchstr(t, "b"); assert(v == nil)
local v = table.intsearchstr(t, "a"); assert(v[1] == 1)
local v = table.intsearchstr(t, "c"); assert(v == nil)

-- test: table size 2
t = {"a","c"}
local v = table.intsearchstr(t, "0"); assert(v == nil)
local v = table.intsearchstr(t, "a"); assert(v[1] == 1)
local v = table.intsearchstr(t, "b"); assert(v == nil)
local v = table.intsearchstr(t, "c"); assert(v[1] == 2)
local v = table.intsearchstr(t, "d"); assert(v == nil)

-- test: typical, with duplicate
t = {"a","b","c","c","d","e","f"}
local v = table.intsearchstr(t, "a"); assert(v[1] == 1)
local v = table.intsearchstr(t, "f"); assert(v[1] == 7)
local v = table.intsearchstr(t, "c"); assert(v[1] == 3 and v[2] == 4)
local v = table.intsearchstr(t, "da"); assert(v == nil)
local v = table.intsearchstr(t, "fa"); assert(v == nil)
local v = table.intsearchstr(t, "0"); assert(v == nil)

-- test: identical
t = {"a","a","a","a","a","a","a","a","a","a"}
local v = table.intsearchstr(t, "a"); assert(v[1] == 1 and v[2] == 10)

-- test: reverse
t = {"f","e","d","c","c","b","a"}
local v = table.intsearchstrrev(t, "d"); assert(v[1] == 3)
local v = table.intsearchstrrev(t, "c"); assert(v[1] == 4 and v[2] == 5)

print "DONE"
```