Rabin-Karp algorithm for Pattern Searching in Matrix

Given matrices txt[][] of dimensions m1 x m2 and pattern pat[][] of dimensions n1 x n2, the task is to check whether a pattern exists in the matrix or not and if yes then print the top mot indices od the pat[][] in txt[][]. It is assumed that m1, m2 ≥ n1, n2

Examples:

Input:
txt[][] = {{G, H, I, P}
           {J, K, L, Q}
           {R, G, H, I}  
           {S, J, K, L}
          }
pat[][] = {{G, H, I},
           {J, K, L}
          }
Output:
Pattern found at ( 0, 0 )
Pattern found at ( 2, 1 )
Explanation:


Input:
txt[][] = { {A, B, C},
            {D, E, F},
            {G, H, I}
          }
pat[][] = { {E, F},
            {H, I}
          }
Output:
Pattern found at (1, 1)

Approach: In order to find a pattern in a 2-D array using Rabin-Karp algorithm, consider an input matrix txt[m1][m2] and a pattern pat[n1][n2]. The idea is to find the hash of each columns of mat[][] and pat[][] and compare the hash values. For any column if hash values are equals than check for the corresponding rows values. Below are the steps:

  1. Find the hash values of each column for the first N1 rows in both txt[][] and pat[][] matrix.
  2. Apply Rabin-Karp Algorithm by finding hash values for the column hashes found in step 1.
  3. If a match is found compare txt[][] and pat[][] matrices for the specific rows and columns.
  4. Else slide down the column hashes by 1 row in the txt matrix using a rolling hash.
  5. Repeat steps 2 to 4 for all the hash values and if we found any pat[][] match in txt[][] then print the indices of top most cell in the txt[][].

To find the hash value: In order to find the hash value of a substring of size N in a text using rolling hash follow below steps:

  1. Remove the first character from the string: hash(txt[s:s+n-1])-(radix**(n-1)*txt[s])%prime_number
  2. Add the next character to the string: hash(txt[s:s+n-1])*radix + txt[n]

Below is the implementation of the above approach:



Python3

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# Python implementation for the 
# pattern matching in 2-D matrix
  
# Function to find the hash-value 
# of the given columns of text
def findHash(arr, col, row):
    hashCol = []
    add = 0
    radix = 256
  
    # For each column
    for i in range(0, col):
  
        for j in reversed(range(0, row)):
            add = add + (radix**(row-j-1) * 
                         ord(arr[j][i]))% 101
        hashCol.append(add % 101);
        add = 0
    return hashCol
  
# Function to check equality of the 
# two strings
def checkEquality(txt, row, col, flag):
    txt = [txt[i][col:patCol + col] 
           for i in range(row, patRow + row)]
  
# If pattern found
    if txt == pat:
        flag = 1
        print("Pattern found at", \
              "(", row, ", ", col, ")")
    return flag
      
# Function to find the hash value of
# of the next column using rolling-hash
# of the Rabin-karp
def colRollingHash(txtHash, nxtRow):
  
    radix = 256
  
    # Find the hash of the matrix
    for j in range(len(txtHash)):
        txtHash[j] = (txtHash[j]*radix \
                      + ord(txt[nxtRow][j]))% 101
        txtHash[j] = txtHash[j] - (radix**(patRow) * 
                     ord(txt[nxtRow-patRow][j]))% 101 
        txtHash[j] = txtHash[j]% 101
    return txtHash
      
  
# Function to match a pattern in 
# the given 2D Matrix
def search(txt, pat):
      
# List of the hashed value for
    # the text and pattern columns
    patHash = []
    txtHash = []
  
    # Hash value of the 
    # pat_hash and txt_hash
    patVal = 0
    txtVal = 0 
  
    # Radix value for the input characters
    radix = 256
      
    # Variable to determine if
    # pattern was found or not
    flag = 0
      
    # Function call to find the
    # hash value of columns
    txtHash = findHash(txt, txtCol, patRow)  
    patHash = findHash(pat, patCol, patRow)
      
    # Calculate hash value for patHash
    for i in range(len(patHash)):
        patVal = patVal \
                 + (radix**(len(patHash)-i-1) * 
                 patHash[i]% 101)
    patVal = patVal % 101
      
      
    # Applying Rabin-Karp to compare
    # txtHash and patHash
    for i in range(patRow-1, txtRow):
        col = 0
        txtVal = 0
          
        # Find the hash value txtHash 
        for j in range(len(patHash)):
            txtVal = txtVal\
                     + (radix**(len(patHash)-j-1) * 
                     txtHash[j])% 101
        txtVal = txtVal % 101
          
        if txtVal == patVal:
            flag = checkEquality(\
                     txt, i + 1-patRow, col, flag)
              
        else:
  
            # Roll the txt window by one character 
            for k in range(len(patHash), len(txtHash)):
  
                txtVal = txtVal \
                         * radix + (txtHash[k])% 101
                txtVal = txtVal \
                         - (radix**(len(patHash)) *
                         (txtHash[k-len(patHash)]))% 101
                txtVal = txtVal % 101
                col = col + 1
  
                # Check if txtVal and patVal are equal
                if patVal == txtVal:
                    flag = checkEquality(\
                           txt, i + 1-patRow, col, flag)   
                else:
                    continue
                  
        # To make sure i does not exceed txtRow
        if i + 1<txtRow:
            txtHash = colRollingHash(txtHash, i + 1)
              
    if flag == 0:
        print("Pattern not found")
      
  
# Driver Code
if __name__ == "__main__":
  
  # Given Text
  txt = [['A', 'B', 'C'], \
         ['D', 'E', 'F'], \
         ['G', 'H', 'I']]
  
  # Given Pattern
  pat = [['E', 'F'], ['H', 'I']]
  
  # Dimensions of the text
  txtRow = 3
  txtCol = 3
  
  # Dimensions for the pattern
  patRow = 2
  patCol = 2
  
  # Function Call
  search(txt, pat)

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Output:

Pattern found at ( 1 ,  1 )
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