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](https://www.geeksforgeeks.org/rabin-karp-algorithm-for-pattern-searching/), consider an input matrix **txt[m1][m2]** and a pattern **pat[n1][n2]**. The idea is to find the [hash](https://www.geeksforgeeks.org/hashing-data-structure/) 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](https://www.geeksforgeeks.org/string-hashing-using-polynomial-rolling-hash-function/).
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]**

#greedy #hash #mathematical #matrix #searching #algorithms