Функционально эквивалентно следующее:
string s;
cin >> s; // Read a string from stdin
size_t pos = s.find('1', 1); // Find the first '1' character in the string starting with the second character
bool pot = ( pos == string::npos ); // pot is true when '1' is not found
// If not found, the answer is half the size of the string rounded down; otherwise it is half the size of the string rounded up
int ans;
if (pot) {
ans = s.size() / 2;
} else {
ans = (s.size() + 1) / 2;
}