In a medical imaging research laboratory, scientists are studying brain scans to identify abnormal

patterns associated with neurological disorders such as Alzheimer$$s disease. They observe that

certain types of lesions and abnormalities often manifest as diagonal patterns in the brain$$s imaging

data. Write an algorithm that automates the abnormality detection process, by analyzing brain scan

data and highlighting regions of the data that exhibit the pattern of a disorder.

You are given brain scan data in the form of a $2$D matrix $$T$$ of size nxn and a pattern of size mxm

$$P$$ that represents the disorder where mxm can be $1$x$1,2$x$2,3$x$3$ up to nxn$.$

Identify the regions where the disorder pattern is found in the data matrix.

Example $1$:

T$=$

A B C B A B C T YF G H J K L H G V

D V T B Y N G B G

F D G A B C V D E

V J O F G H H F W

S R V D V T W F G

K C D E C CC A B C

X Q R T U O F G H

T Y I O B F D V T

P $=$

ABC

FGH

DVT

Example $2$:

A B A B B A D A

A C D A A B B V

C D G B A H K B

G I K C D V F R

Y B J G D B A V

H K G D W C D B

K C D E C C A B

X Q R T U O F G

P $=$

BA

CD

Write $$Rabin$-$Karp$$ string matching algorithm, using $2$ numbers to find modulo while creating

the hash table. Additionally, analyze the time complexity of your algorithm.

Note: You must select those prime numbers that result in the minimum number of spurious hits.

Hint: Traverse through the grid in a diagonal manner to extract the symbols. Instead of going row

by row or column by column, you start from the top$-$left corner and move diagonally, retrieving

each symbol one by one.