LeetCode115—Distinct Subsequences

　原题

链接 Given a string S and a string T, count the number of distinct subsequences of T in S.

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.

分析

子序列的个数．母串 S=s0s1s2…si−2si−1… ，子串 T=t0t1t2…ti−2ti−1… 令 dp(i,j) 表示 {s0s1s2…si−2si−1} 和 {t0t1t2…ti−2ti−1} 的状态 可以列出如下动规方程：

dp(i,j)={dp(i−1,j−1)+dp(i−1,j)dp(i−1,j),s(i−1)==t(j−1),s(i−1)≠t(j−1)

代码

对照方程写出代码即可

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