Python Program for KMP Algorithm for Pattern Searching

Given a text txt[0..n-1] and a pattern pat[0..m-1], write a function search(char pat[], char txt[]) that prints all occurrences of pat[] in txt[]. You may assume that n > m. 
Examples:

Input:  txt[] = "THIS IS A TEST TEXT"
        pat[] = "TEST"
Output: Pattern found at index 10

Input:  txt[] =  "AABAACAADAABAABA"
        pat[] =  "AABA"
Output: Pattern found at index 0
        Pattern found at index 9
        Pattern found at index 12

Pattern searching is an important problem in computer science. When we do search for a string in notepad/word file or browser or database, pattern searching algorithms are used to show the search results. 

Python3

# Python program for KMP Algorithm
def KMPSearch(pat, txt):
    M = len(pat)
    N = len(txt)

    # create lps[] that will hold the longest prefix suffix
    # values for pattern
    lps = [0]*M
    j = 0 # index for pat[]

    # Preprocess the pattern (calculate lps[] array)
    computeLPSArray(pat, M, lps)

    i = 0 # index for txt[]
    while i < N:
        if pat[j] == txt[i]:
            i += 1
            j += 1

        if j == M:
            print ("Found pattern at index", str(i-j))
            j = lps[j-1]

        # mismatch after j matches
        elif i < N and pat[j] != txt[i]:
            # Do not match lps[0..lps[j-1]] characters,
            # they will match anyway
            if j != 0:
                j = lps[j-1]
            else:
                i += 1

def computeLPSArray(pat, M, lps):
    len = 0 # length of the previous longest prefix suffix

    lps[0] # lps[0] is always 0
    i = 1

    # the loop calculates lps[i] for i = 1 to M-1
    while i < M:
        if pat[i]== pat[len]:
            len += 1
            lps[i] = len
            i += 1
        else:
            # This is tricky. Consider the example.
            # AAACAAAA and i = 7. The idea is similar
            # to search step.
            if len != 0:
                len = lps[len-1]

                # Also, note that we do not increment i here
            else:
                lps[i] = 0
                i += 1

txt = "ABABDABACDABABCABAB"
pat = "ABABCABAB"
KMPSearch(pat, txt)

# This code is contributed by Bhavya Jain

Output:

Found pattern at index 10

Time Complexity: O(m+n)

Space Complexity: O(m)

Please refer complete article on KMP Algorithm for Pattern Searching for more details!