Distinct Subsequences (dp)

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.

 题意：求S中所有子串中与T相同的有多少个

空串是任意字符串的子串。

代码：

  class Solution {
  public:
      int numDistinct(string S, string T) {
          int row=S.size()+1;
          int col=T.size()+1;
          vector<int> temp(col,0);
          vector<vector<int>> dp(row,temp);
          dp[0][0]=1;
          for(int i=1;i<row;++i) dp[i][0]=1;

          for(int i=1;i<row;++i){
              for(int j=1;j<=i&&j<col;++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[row-1][col-1];
      }
  };