Lintcode-medium-distinct subsequences

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 was formed from the original string by deleting some (can be none) of the C Haracters without disturbing the relative positions of the remaining characters. (ie, is a subsequence of and is not "ACE" "ABCDE" "AEC" ).

Given S = "rabbbit" , T = "rabbit" , return 3 .

Dynamic programming, with an int two-dimensional array record: The number of different subsequence in the string s before the first J characters (0-j-1) in the first I character (0-i-1)

State transitions:

In either case, the number of times before the first J character in T in S is at least equal to the number of i-1 characters before the first J characters in T, which contains a special case if j = = I, this value is 0

If the j-1 character of T is different from the i-1 character of S, then the addition of one character in S will not change the result, then dp[i][j] = Dp[i-1][j]

If the same, then dp[i][j] on the basis of dp[i-1][j], but also include T in the first j-1 characters in S before the first i-1 characters in the number of occurrences (that is, the last character of the two strings together, and then consider the previous situation), dp[i][j] = Dp[i-1][j ] + dp[i-1][j-1]

 Public classSolution {/**     * @paramS, t:two string. * @return: Count The number of distinct subsequences*/     Public intnumdistinct (String S, String T) {//Write your code here                if(S = =NULL|| S.length () = = 0)            return0; if(T = =NULL|| T.length () = = 0)            return1; intm =s.length (); intn =t.length (); if(N >m)return0; int[] DP =New int[M + 1] [n + 1]; dp[0][0] = 1;  for(inti = 0; I <= m; i++) dp[i][0] = 1;  for(intj = 1; J <= N; J + +){            CharT_end = T.charat (j-1);  for(inti = j; I <= m; i++){                CharS_end = S.charat (i-1); DP[I][J]= Dp[i-1][j]; if(S_end = =t_end) Dp[i][j]+ = Dp[i-1][j-1]; }        }                returnDp[m][n]; }}

Lintcode-medium-distinct subsequences