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Given a string of n characters called the text and a string of k characters called the pattern ( where k n ) . The

Given a string of n characters called the text and a string of k characters called the
pattern (where kn). The following Brute Force algorithm returns the index of the
first character in the text that starts a matching substring or -1 if the search is
unsuccessful (assuming the start index is 1)
ALGORITHM BF-SM (T[1dotsn],P[1dotsk])
// Input: An array T[1dots...n] of n characters representing a text
An array P[1dotsk] of k characters representing a pattern
// Output: The index of the first character in the text that starts a matching substring or -1 if the search is unsuccessful
for i=1ton-k+1do
j=1
while jk and P[j]=T[i+j-1]
a)(3 marks) What is the best-case scenario for the given BF-SM algorithm when searching for a
pattern within a text? provide an example to illustrate this?
b)(2 marks) What is the time complexity of the algorithm in its best-case scenario? (explain
and use Big-0 notation)
c)(3 marks) What is the time complexity of the algorithm when the length of the pattern (k) equals
the length of the text (n) in the best-case scenario? (Explain why)
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