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: 3Explanation: 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: 5Explanation: 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
^^^
Approach #1: DP. [C++]
class Solution {
public:
int numDistinct(string s, string t) {
int ls = s.length();
int lt = t.length();
vector<vector<long>> dp(lt+1, vector<long>(ls+1));
fill(dp[0].begin(), dp[0].end(), 1);
for (int i = 1; i <= lt; ++i) {
for (int j = 1; j <= ls; ++j) {
if (t[i-1] == s[j-1])
dp[i][j] = dp[i-1][j-1] + dp[i][j-1];
else
dp[i][j] = dp[i][j-1];
}
}
return dp[lt][ls];
}
};