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Problem
Given a string S and a string T, count the number of distinct subsequences of S which equals T.
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).
Example 1:
Input: S = “rabbbit”, T = “rabbit”
Output: 3
Explanation:
As shown below, there are 3 ways you can generate “rabbit” from S.(The caret symbol ^ means the chosen letters)
rabbbit
^^^^ ^^
rabbbit
^^ ^^^^
rabbbit
^^^ ^^^
Example 2:
Input: S = “babgbag”, T = “bag”
Output: 5
Explanation:
As shown below, there are 5 ways you can generate “bag” from S.(The caret symbol ^ means the chosen letters)
babgbag
^^ ^
babgbag
^^ ^
babgbag
^ ^^
babgbag
^ ^^
babgbag
^^^
Solution
class Solution {
public int numDistinct(String s, String t) {
int m = s.length(), n = t.length();
if (m < n) return 0;
int[][] dp = new int[m+1][n+1];
for (int i = 0; i <= m; i++) dp[i][0] = 1;
for (int j = 0; j < n; j++) {
for (int i = 0; i < m; i++) {
if (s.charAt(i) == t.charAt(j)) dp[i+1][j+1] = dp[i][j] + dp[i][j+1];
else dp[i+1][j+1] = dp[i][j+1];
}
}
return dp[m][n];
}
}
