Leetcode Week11 Distinct Subsequences

Question

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
    ^^^

Answer

class Solution {
public:
    int numDistinct(string s, string t) {
         vector<vector<int>> dp(t.size(), vector<int>(s.size()));
        int dis = 0;
        for (int i = 0; i < t.size(); i++) {
             dis = 0;
            for (int j = 0; j < s.size(); j++) {
                dp[i][j] = dis;
                if (t[i] == s[j]) {
                    if (i == 0) dis++;
                    else if (j != 0)
                        dis = dp[i - 1][j] + dp[i][j];
                }
            }
        }
        return dis;
    }
};

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