Dashboard - Round 1C 2009 - Google Code Jam

Problem

In A.D. 2100, aliens came to Earth. They wrote a message in a cryptic language, and next to it they wrote a series of symbols. We've come to the conclusion that the symbols indicate a number: the number of seconds before war begins!
Unfortunately we have no idea what each symbol means. We've decided that each symbol indicates one digit, but we aren't sure what each digit means or what base the aliens are using. For example, if they wrote "ab2ac999", they could have meant "31536000" in base 10 -- exactly one year -- or they could have meant "12314555" in base 6 -- 398951 seconds, or about four and a half days. We are sure of three things: the number is positive; like us, the aliens will never start a number with a zero; and they aren't using unary (base 1).
Your job is to determine the minimum possible number of seconds before war begins.

http://wilanw.blogspot.com/2009/09/google-code-jam-round-1c.html
The problem asks us to determine the minimum possible number we can derive from an unknown number representation system. To do this we must assign values to each of the characters present in the symbols. For example let's say we are given "cats" as an input we need to determine what the 'c' means numerically, what the 'a' means numerically etc. Since we want the smallest possible number, it suggests a greedy strategy of assigning what each letter means. In our case, we first see 'c' and therefore wish for this to be as small as possible. However, there is an additional constraint that no number starts with a 0 and since 'c' is the first symbol it cannot be 0. Therefore, the next obvious choice is to give it a value of 1. Next, we process 'a' and assign it a value of 0 since it hasn't been used yet and it's not the first symbol. Following this, 't' gets assigned 2 and 's' gets assigned 3. 

Now the next task is to determine the base system the aliens work on, it can be easily shown we want the base as small as possible - yet large enough to allow us to use all the symbols. Therefore, the base system is simply the number of unique characters/letters in the alien number. We are then tasked with converting this to "human" form (i.e. decimal representation) which can be done iteratively like any base conversion algorithm. Implementation wise, we can keep track of our character assignments in a map data structure. When we encounter a letter, we first check whether or not we have seen the letter - if we haven't then we greedily assign it the next available (and smallest) number. If we have, then we simply skip over the character.

map<char,int> memo;

int main() {
   int nT; cin >> nT;
   string str;
   int k = 1;
   while (nT-- && cin >> str) {
      memo.clear();
      int next = 0;
      memo[str[0]] = 1;
      for (int i = 1; i < str.size(); i++) {
         if (memo.count(str[i]) == 0) {
            memo[str[i]] = next;
            next++;
            if (next == 1) next++;
         }
      }
      long long val = 0;
      int base = next == 0 ? 2 : next;
      for (int i = 0; i < str.size(); i++) {
         val = val * base + memo[str[i]];
      }
      cout << "Case #" << k << ": " << val << "\n";
      k++;
   }
   return 0;
}

Read full article from Dashboard - Round 1C 2009 - Google Code Jam