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: 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 ^^^
考察：dp；
class Solution {
public:
int numDistinct(string s, string t) {
if (s.empty() || t.empty())
return 0;
vector<vector<long>> dp(t.size()+1, vector<long>(s.size()+1, 0));
for (int i = 0; i <= s.size(); i ++)
dp[0][i] = 1;
for (int i = 1; i <= t.size(); i ++)
dp[i][0] = 0;
for (int i = 1; i <= t.size(); i ++) {
for (int j = 1; j <= s.size(); j ++)
dp[i][j] = dp[i][j-1] + (t[i-1] == s[j-1] ? dp[i-1][j-1] : 0);
}
return dp.back().back();
}
};