115. Distinct Subsequences

• Difficulty: Hard

• Topics: String, Dynamic Programming

• Similar Questions:

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
    ^^^

Solutions:

class Solution {
public:
    int numDistinct(string s, string t) {
        int sLen = s.length();
        int tLen = t.length();

        vector<vector<long>> dp(sLen + 1, vector<long> (tLen + 1, 0));
        dp[0][0] = 1;

        for (int i = 1; i <= sLen; ++i) {
            dp[i][0] = 1;
        }

        for (int j = 1; j <= tLen; ++j) {
            dp[0][j] = 0;
        }

        for (int i = 1; i <= sLen; ++i) {
            for (int j = 1; j <=tLen; ++j) {
                dp[i][j] = dp[i-1][j];
                if (s[i-1] == t[j-1]) {
                    dp[i][j] += dp[i-1][j-1];
                }
            }
        }
        return dp[sLen][tLen];
    }
};