leetcode-distinct sequences

Solution: when see question about two strings , DP should be considered first.

We can abstract this question to calculate appear times for string T with length i in string S with length j, which can be represented by numbers[i][j], then through observation and thinking , we can know for numbers[i][j] it should at least equal the numbers[i][j-1] and if T.charAt(i)==S.charAt(j) , numbers[i][j] should also be add numbers[i-1][j-1]

 

class Solution
{
public:
    int numDistinct(string S, string T) {
        int sLen = S.length(); int tLen = T.length();
        vector<vector<int>> dp(sLen+1,vector<int>(tLen+1));//dp[i][j]表示对应S前i个和T前j个字符的子问题。
        for (int i = 0; i <= sLen; i++) dp[i][0] = 1;
        for (int i = 1; i <= sLen; i++)
        {
            for (int j = 1; j <= tLen; j++)
            {
                if (S[i - 1] == T[j - 1])
                {
                    dp[i][j] = dp[i - 1][j] + dp[i-1][j-1];
                }
                else
                {
                    dp[i][j] = dp[i-1][j];
                }
            }
        }
        return dp[sLen][tLen];
    }

};
int main()
{
    Solution s;
    string strS("b");
    string strT("a");
    cout << s.numDistinct(strS, strT) << endl;
    return 0;
}

 http://rleetcode.blogspot.com/2014/01/distinct-subsequences-java.html