My solution in Java:
public static String compute(Collection strings) {
if(strings.isEmpty()) return "";
Set v = new HashSet();
int i = 0;
try {
while(true) {
for(String s : strings) v.add(s.charAt(i));
if(v.size() > 1) break;
v.clear();
i++;
}
} catch(StringIndexOutOfBoundsException ex) {}
return strings.iterator().next().substring(0, i);
}