38. Count and Say (String; DP)

The count-and-say sequence is the sequence of integers beginning as follows:
1, 11, 21, 1211, 111221, ...

1 is read off as "one 1" or 11.
11 is read off as "two 1s" or 21.
21 is read off as "one 2, then one 1" or 1211.

Given an integer n, generate the nth sequence.

Note: The sequence of integers will be represented as a string.

思路：序列问题，用动态规划存储上一个状态，从而能够推导出下一个元素

class Solution {
public:
    string countAndSay(int n) {
        string previous = "1";
        string current = "";
        string tmp;
        stringstream ss;
        int times;
        for(int i = 2; i <= n; i++){ //从头开始推导序列中每个元素
            for(int j = 0; j < previous.length(); j++){ //遍历前一个元素中的每一位
                times = 1;
                while(j+1 < previous.length()&&previous[j+1]==previous[j]){
                    times++;
                    j++;
                }
                ss.clear();
                ss << times;
                ss >> tmp;
                current.append(tmp);
                ss.clear();
                ss << previous[j];
                ss >> tmp;
                current.append(tmp);
            }
            previous = current;
            current = "";
        }
        return previous;
    }
};