Python Implementation of KMP algorithm.

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Haystack: The string in which given pattern needs to be searched. Needle: The pattern to be searched.

Time complexity: Search portion (strstr method) has the complexity O(n) where n is the length of haystack but as needle is also pre parsed for building prefix table O(m) is required for building prefix table where m is the length of the needle. Therefore, overall time complexity for KMP is O(n+m) Space complexity: O(m) because of prefix table on needle.

Note: Following implementation returns the start position of match in haystack (if there is a match) else returns -1, for edge cases like if needle/haystack is an empty string or needle is not found in haystack.

def get_prefix_table(needle):
    prefix_set = set()
    n = len(needle)
    prefix_table = [0]*n
    delimeter = 1
        j = 1
            if needle[j:delimeter+1] in prefix_set:
                prefix_table[delimeter] = delimeter - j + 1
            j += 1
        delimeter += 1
    return prefix_table

def strstr(haystack, needle):
    # m: denoting the position within S where the prospective match for W begins
    # i: denoting the index of the currently considered character in W.
    haystack_len = len(haystack)
    needle_len = len(needle)
    if (needle_len > haystack_len) or (not haystack_len) or (not needle_len):
        return -1
    prefix_table = get_prefix_table(needle)
    m = i = 0
    while((i<needle_len) and (m<haystack_len)):
        if haystack[m] == needle[i]:
            i += 1
            m += 1
            if i != 0:
                i = prefix_table[i-1]
                m += 1
    if i==needle_len and haystack[m-1] == needle[i-1]:
        return m - needle_len
        return -1

if __name__ == '__main__':
    needle = 'abcaby'
    haystack = 'abxabcabcaby'
    print strstr(haystack, needle)

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