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
.
dp[i][j] stands for the number of distince subsequences of T(First i characters) in S(First j characters)...
class Solution {
public:
int numDistinct(string S, string T) {
// Note: The Solution object is instantiated only once and is reused by each test case.
vector< vector<int> > dp;
vector<int> row(S.length()+1,0);
vector<int> ones(S.length()+1,1);
int i,j;
if(S.length()<T.length())
return 0;
else{
dp.push_back(ones);
for(i=1;i<=T.length();i++)
dp.push_back(row);
for(i=1;i<=T.length();i++){
for(j=i;j<=S.length();j++)
if( T[i-1]==S[j-1] )
dp[i][j]=dp[i][j-1]+dp[i-1][j-1];
else
dp[i][j]=dp[i][j-1];
}
}
return dp[T.length()][S.length()];
}
};