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# 53. Distinct Subsequences

Count the number of longest common subsequence

Given two strings `s` and `t`, return *the number of distinct subsequences of `s` which equals `t`*.

A string's **subsequence** is a new string formed from the original string by deleting some (can be none) of the characters without disturbing the remaining characters' relative positions. (i.e., `"ACE"` is a subsequence of `"ABCDE"` while `"AEC"` is not).

It is guaranteed the answer fits on a 32-bit signed integer.

**Example 1:**

```
Input: s = "rabbbit", t = "rabbit"
Output: 3
Explanation:
As shown below, there are 3 ways you can generate "rabbit" from S.
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.
babgbag
babgbag
babgbag
babgbag
babgbag
```

## Solution: (Dp)

```cpp
class Solution
{
public:
    int numDistinct(string s, string t)
    {

        int n = s.length();
        int m = t.length();

        vector<vector<long long unsigned>> dp(n + 1, vector<long long unsigned>(m + 1, 0));

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

        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= m; j++)
            {

                if (s[i - 1] == t[j - 1])
                {
                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
                }
                else
                {
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }

        return dp[n][m];
    }
};
```