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The original KMP Algorithm has the runtime complexity of O (M + N) and auxiliary space O (M), where N is the size of the input text and M is the size of the pattern. Preprocessing step costs O (M) time.What is the use of LPs in KMP?
KMP algorithm preprocesses pat  and constructs an auxiliary lps  of size m (same as size of pattern) which is used to skip characters while matching. name lps indicates longest proper prefix which is also suffix.. A proper prefix is prefix with whole string not allowed. For example, prefixes of “ABC” are “”, “A”, “AB” and “ABC”.How does Knuth-Morris-Pratt (KMP) algorithm work?
From the previous article, it is known that KMP (a.k.a. Knuth-Morris-Pratt) algorithm preprocesses the pattern P and constructs a failure function F (also called as lps ) to store the length of the longest suffix of the sub-pattern P [1..l], which is also a prefix of P, for l = 0 to m-1.Is it possible to skip the fourth and fifth matching in KMP?
If we can skip the fourth and fifth matching, then the original KMP algorithm can further be optimised to answer the real-time queries. Real-time Optimization: The term real-time in this case can be interpreted as checking each character in the text T at most once.