awk print line of file2 based on condition of file1 - awk

Question

I have two files:
cat file1:
0 xxx
1 yyy
1 zzz
0 aaa
cat file2:
A bbb
B ccc
C ddd
D eee
How do I get the following output using awk:
B ccc
C ddd
My question is, how do I print lines from file2 only if a certain field in file1 (i.e. field 1) matches a certain value (i.e. 1)?
Additional information:
Files file1 and file2 have an equal number of lines.
Files file1 and file2 have millions of lines and cannot be read into memory.
file1 has 4 columns.
file2 has approximately 1000 columns.

Answer 1

Try doing this (a bit obfuscated):
awk 'NR==FNR{a[NR]=$1}NR!=FNR&&a[FNR]' file1 file2
On multiples lines it can be clearer (reminder, awk works like this : condition{action} :
awk '
NR==FNR{arr[NR]=$1}
NR!=FNR && arr[FNR]
' file1 file2
If I remove the "clever" parts of the snippet :
awk '
if (NR == FNR) {arr[NR]=$1}
if (NR != FNR && arr[FNR]) {print $0}
' file1 file2
When awk find a condition alone (without action) like NR!=FNR && arr[FNR], it print by default on STDOUT implicitly is the expressions is TRUE (> 0)
Explanations
NR is the number of the current record from the start of input
FNR is the ordinal number of the current record in the current file (so NR is different than FNR on the second file)
arr[NR]=$1 : feeding array arr with indice of the current NR with the first column
if NR!=FNR we are in the next file and if the value of the array if 1, then we print

Answer 2

No as clean as a awk solution
$ paste file2 file1 | sed '/0/d' | cut -f1
B
C
You mentioned something about millions of lines, in order to just do a single pass through the files, I'd resort to python. Something like this perhaps (python 2.7):
with open("file1") as fd1, open("file2") as fd2:
for l1, l2 in zip(fd1, fd2):
if not l1.startswith('0'):
print l2.strip()

Answer 3

awk '{
getline value <"file2";
if ($1)
print value;
}' file1