Naive String Matching

Naive(T, P)
   n = length(T)
   m = length(P)
   for s = 0 to n-m                     O(n-m+1)
      if P[1..m] = T[s+1..s+m]              O(m)
      then print "Pattern occurs with shift" s

This algorithm takes O((n-m+1)m) time.

Example

However, there is more information in a failed match:

T:	a	a	a	a	b	a	a	...
P:	a	a	a	a	a

s = s + m

No need to consider s+1, .., s+(m-1)