Page: THE KNUTH-MORRIS-PRATT ALGORITHM
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Knuth-Morris-Pratt Algorithm. Knuth Morris Pratt (KMP) is an algorithm, which checks the characters from left to right. When a pattern has a sub-pattern appears more than one in the sub-pattern, it uses that property to improve the time complexity, also for in the worst case

KMP algorithm is used to find a "Pattern" in a "Text". This algorithm campers character by character from left to right. But whenever a mismatch occurs, it uses a preprocessed table called "Prefix Table" to skip characters comparison while matching. Some times prefix table is also known as LPS Table. Here LPS stands for "Longest proper Prefix which is also Suffix".

Steps for Creating LPS Table (Prefix Table)

• Step 1 - Define a one dimensional array with the size equal to the length of the Pattern. (LPS[size])

• Step 2 - Define variables i & j. Set i = 0, j = 1 and LPS[0] = 0

• Step 3 - Compare the characters at Pattern[i] and Pattern[j]

• Step 4 - If both are matched then set LPS[j] = i+1 and increment both i & j values by one. Goto to Step 3.

• Step 5 - If both are not matched then check the value of variable 'i'. If it is '0' then set LPS[j] = 0 and increment 'j' value by one, if it is not '0' then set i = LPS[i-1]. Goto Step 3.

• Step 6- Repeat above steps until all the values of LPS[] are filled.

Let us use above steps to create prefix table for a pattern...

How to use LPS Table

• We use the LPS table to decide that how many characters are to be skipped for comparison when a mismatch is occured.

• When a mismatch occurs, check the LPS value of previous character of the mismatched character in the pattern. If it is '0' then start comparing first character of the pattern with next character to the mismatched character in the text.

• If it is not '0' then start comparing the character which is at index value equal to the LPS value of previous character to the mismatched character in pattern with the mismatched character in the Text.

How the KMP Algorithm Works

Let us see a working example of KMP Algorithm to find a Pattern in a Text...

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