115. Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of S which equals T.A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).Here is an example:S = "rabbbit", T = "rabbit"Return 3.

• 这道题目基本上靠自己推理出来的，觉得还是挺有意思。主要的关键是抓住递推公式。
• dp[i][j] 表示数列s[i],t[j]的最大数目。则这时dp[i][j] = dp[i-1][j] + dp[i-1][j-1] (s[i] =t[j]);如果删除是s[i],则这时dp[i][j] = dp[i-1][j],如果保留s[i],则需要满足s[i] = t[j];

class Solution {public:    int numDistinct(string s, string t) {        int n = s.size();        int m = t.size();        if(n < m){            return 0;        }        vector<int> cnt(m+1,0);        vector<vector<int>> dp(n+1,cnt);        for(int i = 0;i <= n; ++i){            dp[i][0] = 1;        }        for(int i = 1;i <= n ; ++i){            for(int j = 1;j <= i&& j <= m; ++j){                dp[i][j] = dp[i-1][j] + (s[i-1] == t[j-1]?dp[i-1][j-1]:0);             }        }        return dp[n][m];    }};