grep lines matching a pattern, and the lines before and after the matching until different pattern

Question

Start_pattern
abc
d End_pattern
Start_pattern
abc
d
ef
ghij 
klm
no End_pattern
Start_pattern
abc
def
hij End_pattern
Start_pattern
abc
dhi
jklm End_pattern

Answer 1

$ cat tst.awk
/Start_pattern/ { fnd=1; buf="" }
fnd {
    buf = buf $0 ORS
    if (/End_pattern/) {
        if (buf ~ /ef/) {
            printf "%s", buf
        }
        fnd = 0
        buf = ""
    }
}

$ awk -f tst.awk file
Start_pattern
abc
d
ef
ghij
klm
no End_pattern
Start_pattern
abc
def
hij End_pattern