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Problem Distinct Subsequence
Problem Desciption : 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.
Solution : 采用动态编程 (Dynamic Programming)的思路。mat[i][j]表示子问题S = S.substring(0, i-1), T= T.substring(0,j-1)的结果
1 public int numDistinct(String S, String T) { 2 int slen = S.length(); 3 int tlen = T.length(); 4 if (slen == 0) return 0; 5 if (tlen == 0) return 1; 6 int[][] mat = new int[slen + 1][tlen +1]; 7 for (int i = 0; i <= slen; i++) mat[i][0] = 1; 8 for (int i = 1; i <= slen; i++) 9 for (int j = 1; j <= tlen; j++) {10 if (S.charAt(i-1) == T.charAt(j-1))11 mat[i][j] = mat[i-1][j-1] + mat[i-1][j];12 else 13 mat[i][j] = mat[i-1][j];14 }15 16 return mat[slen][tlen];17 }
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