LeetCode-Distinct Subsequences

典型的dp，

最开始写了个递归的，过不了大数据，

class Solution {
public:
    int numDistinct(string S, string T) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int m = S.length();
        int n = T.length();
        return getDistinct(S, T, m - 1, n - 1);
    }
    int getDistinct(string &S, string &T, int i, int j) {
        if (j < 0) {
            return 1;
        }
        if (i < 0) {
            return 0;
        }
        if (j > i) {
            return 0;
        }
        if (S[i] == T[j]) {
            return (getDistinct(S, T, i - 1, j - 1) + getDistinct(S, T, i - 1, j));
        }
        return getDistinct(S, T, i - 1, j);
    }
};

哎，看来做DP的题目的第一选择就应该是直接用数组保存最优解。

class Solution {
public:
    int numDistinct(string S, string T) {
        int N = S.size(), M = T.size();
        int dp[M+1][N+1];
        dp[0][0] = 1;
        for (int j = 1; j <= N; ++j)
            dp[0][j] = 1;
        for (int i = 1; i <= M; ++i)
            dp[i][0] = 0;

        for (int i = 1; i <= M; ++i)
            for (int j = 1; j <= N; ++j)
                if (S[j-1] == T[i-1])
                    dp[i][j] = dp[i][j-1] + dp[i-1][j-1];
                else
                    dp[i][j] = dp[i][j-1];

        return dp[M][N];
    }
};