match between two files and merge the output using awk - python-3.x

Question

I have two files.First column is common between the both files and I would like to merge the file and generate the output where its copy the first file third column every time in second file whenever there is match.
file1
412234;mark
413234;raja
file2
412234;value1
412234;value2
412234;value3
412234;value4
413234;value1
413234;value2
413234;value3
Output file
412234;value1;mark
412234;value2;mark
412234;value3;mark
412234;value4;mark
413234;value1;raja
413234;value2;raja
413234;value3;raja

Answer 1

Try this:
awk -F';' 'BEGIN{FS=OFS=";"} FNR==NR{a[$1]=$2; next} ($1 in a){print $1, $2, a[$1]}' file1 file2
explanation:
-F';' means that AWK will use ; as field separator;
BEGIN{FS=OFS=";"} set the Output filed separator, used by print function;
AWK parse all files sequentially, the condition:
FNR==NR
is true only when parsing the first file.
While parsing file1, it saves a vector a with first match as index and second match as value;
a is expected to be
a[412234] = mark
a[413234] = raja
($1 in a) is the condition to met, true when first match on file2 is found on vector a.
If true then execute:
print $1";"$2";"a[$1]
that prints matches from file2 and the value of the vector a, saved from file1
----- EDIT
In case file1 contains multiple lines with same index, you need to save all distinct values in a vector and then scan the whole vector for multiple matches on file2
awk -F';' ' \
function vlen(a){n=0; for(i in a) n++; return n;} # helper function defined here \
function contained(val, vect) {found =0; for (x in vect) { if(vect[x] == val) found=1}; return found} # helper function defined here \
BEGIN{FS=OFS=";"} # Set output field separator \
FNR==NR{n=vlen(a); a[n]=$1; b[n]=$2; next} # scan file1 and save all indexes and value in different vectors \
{if(contained($1,a)) { for (i in a) { if (a[i] == $1) { print $1, $2, b[i]}} } else { print $1, $2 } } # for each line in file2, scan the whole vector a looking for a match \
' file1 file2
here we are defining the vlen and contained helper functions

Answer 2

Would you try the following:
awk '
BEGIN {FS=OFS=";"}
NR==FNR {
c[$1]++
a[$1,c[$1]]=$2
next
}
{
if (c[$1]) {
for (i=1; i<=c[$1]; i++) {
$3=a[$1,i]; print
}
} else {
print
}
}' file1 file2
Result with the file1 and file2 provided in the OP's last comment:
412234;value1;mark
412234;value1;raja
412234;value2;mark
412234;value2;raja
413234;value1
413234;value2
If the index in the 1st column (such as 412234) appears more than once
in file1, we need to preserve the existing value in the 2nd column
(such as mark) without overwriting.
Then an array c is introduced to count the occurrences of the index.
Note that the order of the result differs from the OP's expected output.
I hope it is acceptable.