[Leetcode]Distinct Subsequences

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思路：计数问题往往用DP

class Solution {public:    int numDistinct(string S, string T) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        vector<vector<int> > f(S.size()+1, vector<int>(T.size()+1, 0));        for(int i = 0; i <= S.size(); ++i)            f[i][T.size()] = 1;        for(int i = S.size()-1; i >= 0; --i)            for(int j = T.size()-1; j >= 0; --j)                f[i][j] = f[i+1][j] + (S[i] == T[j])*f[i+1][j+1];        return f[0][0];    }};

优化空间

class Solution {public:    int numDistinct(string S, string T) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        vector<int> f(T.size()+1);        f[T.size()] = 1;        for(int i = S.size()-1; i >= 0; --i)            for(int j = 0; j < T.size(); ++j)                f[j] += (S[i] == T[j]) * f[j+1];        return f[0];    }};