Introduction: $($Assembly MIPS$32)($SOME ERRORS I GOT FROM OTHER SOLUTIONS: Runtime exception at $0$x$0040001$c: address out of range $0$x$00000000,$ "max" is not a recognized operator the solution with errors is provided$)$

$.$data

s$1\_$prompt: $.$asciiz "Enter the first string $($max $1024$ characters$)$: $"$

s$2\_$prompt: $.$asciiz "Enter the second string $($max $1024$ characters$)$: $"$

lcs$\_$result: $.$asciiz "The length of LCS is $"$

$.$text

$.$globl main

main:

# Prompt user for the first string

li $v$0,4$

la $a$0,$ s$1\_$prompt

syscall

# Read the first string from the user

li $v$0,8$

la $a$0,0$ # Buffer address

li $a$1,1024$ # Buffer size

syscall

# Prompt user for the second string

li $v$0,4$

la $a$0,$ s$2\_$prompt

syscall

# Read the second string from the user

li $v$0,8$

la $a$0,0$ # Buffer address

li $a$1,1024$ # Buffer size

syscall

# Call find$\_$lcs function

la $a$0,0$ # Address of the first string

la $a$1,0$ # Address of the second string

jal find$\_$lcs # Jump and link to find$\_$lcs function

# Print the result

li $v$0,4$

la $a$0,$ lcs$\_$result

syscall

# Print the length of LCS

li $v$0,1$

move $a$0,$ $v$0$ # The length of LCS is stored in $v$0$

syscall

# Exit program

li $v$0,10$

syscall

# Recursive function to find the length of LCS

# Input: $a$0-$ address of the first string

# $a$1-$ address of the second string

find$\_$lcs:

lb $t$0,0($$a$0)$ # Load the first character from the first string

lb $t$1,0($$a$1)$ # Load the first character from the second string

beq $t$0,$ $zero, exit$\_$find$\_$lcs # If end of string $1$ is reached, return $0$

beq $t$1,$ $zero, exit$\_$find$\_$lcs # If end of string $2$ is reached, return $0$

beq $t$0,$ $t$1,$ matching$\_$chars # If characters match, jump to matching$\_$chars

j non$\_$matching$\_$chars

matching$\_$chars:

addi $a$0,$ $a$0,1$ # Move to the next character in string $1$

addi $a$1,$ $a$1,1$ # Move to the next character in string $2$

jal find$\_$lcs # Recursive call

addi $v$0,$ $v$0,1$ # Increment result by $1($matching character$)$

j exit$\_$find$\_$lcs

non$\_$matching$\_$chars:

addi $a$0,$ $a$0,1$ # Move to the next character in string $1$

jal find$\_$lcs # Recursive call

move $t$2,$ $v$0$ # Store result in $t$2$

addi $a$0,$ $a$0,-1$ # Backtrack to the previous character in string $1$

addi $a$1,$ $a$1,1$ # Move to the next character in string $2$

jal find$\_$lcs # Recursive call

move $t$3,$ $v$0$ # Store result in $t$3$

max $v$0,$ $t$2,$ $t$3$ # Select the maximum of the two results

j exit$\_$find$\_$lcs

exit$\_$find$\_$lcs:

jr $ra

Logest Common Sequence $($LCS$)$ is the longest subsequence that is common in two given sequences, provided that the elements of the subsequence are not required to occupy consecutive positions within the original sequences. LCS is used in compressing genome resequencing data and to authenticate users within their mobile phone through in$-$air signatures

Implementation:

Define Function: find$\_$lcs

Inputs:

$,s1,$ an address of the first null$-$terminated string in Register $$a0.$

$,$ S$2,$ an address of the second null$-$terminated string in Register $a$1$

Outputs:

$,N,$ the size of the longest common sequence in Register $$v0.$

You are asked to write recursive function that find the LCS between two null$-$terminated strings. The function receives the address of two strings S$1$ and S$2$ as a parameter and return the length of the longest common sequence as an output. The label of the function should be declared as global $($i$.$e$.$ can be called from another file$).$ Refer to the $C$ code given below:

int find$\_$lcs$($string s$1,$ string s$2)$

$\{$

if