Saturday, January 25, 2014

Distinct Subsequences (Java)


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: when see question about two strings , DP should be considered first. we can abstract this question to calculate appear times for string T with length i in string S with length j, which can be represented by numbers[i][j], then through observation and thinking , we can know for numbers[i][j] it should at least equal the numbers[i][j-1] and if T.charAt(i)==S.charAt(j) , numbers[i][j] should also be add numbers[i-1][j-1]