Thread: subsequences

Hi All: can Anybody explain to me in details how you get this solution. I am not getting it. Thanks

Problem: 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:

public int numDistincts(String S, String T) {
int[][] table = new int[S.length() + 1][T.length() + 1];

for (int i = 0; i < S.length(); i++)
table[i][0] = 1;

for (int i = 1; i <= S.length(); i++) {
for (int j = 1; j <= T.length(); j++) {
if (S.charAt(i - 1) == T.charAt(j - 1)) {
table[i][j] += table[i - 1][j] + table[i - 1][j - 1];
} else {
table[i][j] += table[i - 1][j];
}
}
}

return table[S.length()][T.length()];
}

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