99 lines
2.7 KiB
Python
99 lines
2.7 KiB
Python
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'''
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String pattern matching algorithm which performs efficiently for large text and patterns
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Algorithm:
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Rabin Karp works on the concept of hashing. If the substring of the given text
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is same as the pattern then the corresponding hash value should also be same. Exploiting this idea
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and designing a hash function which can be computed in O(m) time for both pattern and initial window
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of text. The subsequent window each will require only O(1) time. And we slide the window n-m times
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after the initial window. Therefore the overall complexity of calculating hash function for text is O(n-m+1)
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Once the hash value matches, the underlying string is again checked with pattern for matching
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Complexity:
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Best case: O(n-m+1)
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Worst case: O(nm)
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'''
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def rabin_karp(T: str, P: str, q: int ,d: int = 256) -> None :
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'''
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Parameters:
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T: string
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The string where the pattern needs to be searched
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P: string
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The pattern to be searched
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q: int
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An appropriately chosen prime number based on length of input strings
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The higher the prime number, the lower the collisions and spurious hits
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d: int, default value 256
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Denotes the no of unique character that is used for encoding
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Example:
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>>> pos = rabin_karp("AAEXCRTDDEAAFT","AA",101)
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Pattern found at pos: 0
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Pattern found at pos: 10
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'''
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n = len(T) # length of text
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m = len(P) # length of pattern
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p=0 # Hash value of pattern
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t=0 # Hash value of text
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#Computing h: (h=d^m-1 mod q)
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h=1
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for i in range(1,m):
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h = (h*d)%q
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#Computing hash value of pattern and initial window (of size m) of text
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for j in range(m):
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p = (d*p + ord(P[j])) % q
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t = (d*t + ord(T[j])) % q
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found = False
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pos=[] # To store positions
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#Sliding window and matching
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for s in range(n-m+1):
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if p==t: # if hash value matches
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if P == T[s:s+m]: # check for string match
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pos.append(s)
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if not found:
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found = True
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if s<n-m:
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t = (d*(t-ord(T[s])*h) + ord(T[s+m])) % q # updating hash value of t for next window
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if t<0:
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t = t+q # To make sure t is positive integer
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if not found: # If pattern not found in text
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pos.append(-1)
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#Printing results
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if pos[0]==-1:
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print("Pattern not found")
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else:
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for i in pos:
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print(f"Pattern found at pos: {i}")
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if __name__ == "__main__":
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T = "AAEXCRTDDEAAFT"
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P = "AA"
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rabin_karp(T,P,101)
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