Algorithm to find whether a given Pattern is present in Text or not and return the index if the pattern is found.

1. Naïve String Matching Algorithm
Dr. Kiran K
Assistant Professor
Department of CSE
UVCE
Bengaluru, India.

2. Introduction
T [1 . . n] : Text of length n.
P [1 . . m] : Pattern of length m.
∑ : A Finite Alphabet consisting of characters from which the elements of
P and T are drawn.
Eg.: ∑ = {0, 1}
∑ = {a, b, . . . , z}
String-Matching Problem:
Find All Valid Shifts with which a given Pattern P occurs in a given Text T.
Strings of Characters

3. Introduction…
Shift (s): A Pattern P is said to occur with shift s in text T, if 0 ≤ s ≤ n – m and
T [s + 1 . . s + m] = P [1 . . m]. (T [s + j] = P [j] for 1 ≤ j ≤ m)
P occurs beginning at position s + 1 in text T.
• Valid Shift: P occurs with shift s in T.
• Invalid Shift: P does not occur in T.
String-matching algorithms generally perform some Preprocessing based on the pattern and
then finds all Valid Shifts (Matching).

4. Algorithm
Finds All Valid Shifts using a loop that checks the condition:
P [1 . . m] = T [s + 1 . . s + m] for each of the n – m + 1 possible values of s.
NAIVE-STRING-MATCHER (T, P)
n = T.length
l = P.length
For (s = 0 to n – m)
If (P [1 . . m] = T [s + 1 . . s + m])
Print “Pattern occurs with shift s”
Running Time:
Worst Case: Ө ((n – m + 1) m)
Best Case: Ө (n + m)

5. References:
• Thomas H Cormen. Charles E Leiserson, Ronald L Rivest, Clifford Stein,
Introduction to Algorithms, Third Edition, The MIT Press Cambridge,
Massachusetts London, England.