A Fast String Searching Algorithm
An algorithm is presented that searches for
the location, "i," of the first occurrence of a 
character string, "pat," in another string, "string."
 During the search operation, the characters of 
pat are matched starting with the last character of
pat.  The information gained by starting the match 
at the end of the pattern often allows the algorithm
to proceed in large jumps through the text being 
searched.  Thus the algorithm has the unusual property that,
in most cases, not all of the first i characters 
of string are inspected.  The number of characters actually
inspected (on the average) decreases as a 
function of the length of pat.  For a random English
pattern of length 5, the algorithm will typically 
inspect i/4 characters of string before finding a match at
i.  Furthermore, the algorithm has been implemented 
so that (on the average) fewer than i+patlen machine
instructions are executed.  These conclusions are 
supported with empirical evidence and a theoretical
analysis of the average behavior of the algorithm. 
 The worst case behavior of the algorithm is linear in
i+patlen, assuming the availability of array space 
for tables linear in patlen plus the size of the alphabet.
CACM October, 1977
Boyer, R. S.
