64 lines
2.4 KiB
Lua
64 lines
2.4 KiB
Lua
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-- Rabin–Karp substring s search in string t
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-- https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm
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-- rnd 2017
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-- ALGORITHM:
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-- 1.) loop compute hashes of all substrings of t of length |s| using rolling hash idea
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-- 2.) if some hash matches hash of s check more closely ( waste |s| time here, so this should only occur with probability < O(1)/|s| so expected waste is O(1))
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-- how to do 1) rolling hash: how does hash of string change if you remove first character and add new last character? ... dont need to recompute whole hash!
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-- summary: we end up using O(|t|+|s| + (number of needed hits)*O(1)) time (if you want more than 1 hit..)
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-- this is big improvement compared to O(|t|*|s|) when doing naive substring search
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-- improvement: we could also precompute all substring hashes of length |s| and then compute hash of some string of same length and
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-- do quick lookups for that hash ( hash of hash :) )
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if not hash then
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hash = function(s,p)
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local length = string.len(s);
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local h = 0 ;
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for i = 1, length do
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h=(256*h + string.byte(s,i))%p
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end
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return h%p
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end
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getpower = function(p,k) -- safe computation of power 256^k in mod p arithmetic
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local r=1; for i = 1,k do r=(256*r) % p end; return r
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end
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karpin_rabin = function(t,s)
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local ls = string.len(s);
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local lt = string.len(t);
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if lt<ls then return nil end
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local p = 10011;
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local hs = hash(s,p);
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local rht = hash(string.sub(t,1,ls),p); -- rolling hash
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if hs == rht then
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if s == string.sub(t,1,ls) then return 1 end -- match at position 1!
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end
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local power256 = getpower(p,ls-1);
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for i = 2,lt-ls+1 do
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local c1 = string.byte(t,i-1); local c2 = string.byte(t,i+ls-1);
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rht = (256*(rht - c1*power256)+c2)%p; -- update rolling hash to hash of next substring; this is ok since: a===b then also a*c===b*c
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if hs == rht then
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if s == string.sub(t,i,i+ls-1) then return i end -- match at position i!
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end
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end
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return nil
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end
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local t = "The Rabin–Karp algorithm is inferior for single pattern searching to Knuth–Morris–Pratt algorithm, Boyer–Moore string search algorithm and other faster single pattern string searching algorithms because of its slow worst case behavior. However, it is an algorithm of choice for multiple pattern search.";
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local s = "inferior";
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local chk = karpin_rabin(t,s)
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if chk then say("found '" .. s .. "' in text pos. " .. chk .." : ..." .. string.sub(t,chk,chk+50) .. "...")
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else say("could not find '"..s.."' in text")
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end
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end
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