# 115. Distinct Subsequences

## Problem

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).

The test cases are generated so that 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
```

## Code

```
class Solution {
public int numDistinct(String s, String t) {
int m = s.length();
int n = t.length();
int[][] dp = new int[m + 1][n + 1];
for(int i = 0; i <= m; i++){
dp[i][0] = 1;
}
for(int i = 1; i <= m; i++){
for(int j = 1; j <= n; j++){
if(s.charAt(i - 1) == t.charAt(j - 1)){
dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
} else {
dp[i][j] = dp[i - 1][j];
}
}
}
return dp[m][n];
}
}
```

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