++counters[s];

is the same as:

++(counters.operator[](s))


---------------------


std::map<int,double> cats;
cats[100] = 10.0;
cats[100000] = sqrt(100000);
cats[5] = sqrt(5);
cats[505] = sqrt(505);

for (std::map<int,double>::const_iterator itr = cats.begin(); 
     itr != cats.end();itr++) {
  std::cout << (*itr).first << " " << itr->second << std::endl;
} 


---------------------


int main() {
    std::string s;
    // store each word and an associated count
    std::map<std::string, int> counters; 
    // read the input, keeping track of each word and how often we see it

    // n is # of rows currently in table/map
    while (std::cin >> s) {
      //++counters[s];
      std::map<std::string,int>::iterator itr = counters.find(s);  // O(log n)
      if (itr == counters.end()) {
        // not yet seen this word
        std::pair<const std::string,int> my_pair(s,1); 
        counters.insert(my_pair);  // O(log n)
        // also the same thing:
        //counters.insert(std::pair<const std::string,int>(s,1));
        //counters.insert(std::make_pair(s,1));
      } else {
        // increment the pair
        assert (itr->first == s);
        ++itr->second;  // O(1)
        //++counters[s];
      }
    }

    // write the words and associated counts
    std::map<std::string, int>::const_iterator it;
    for (it = counters.begin(); it != counters.end(); ++it) {
      std::cout << it->first << "\t" << it->second << std::endl;
    }
    return 0; 
}