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Double Sequence IV

Description

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).

https://leetcode.com/problems/distinct-subsequences/description/

Example I:

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 II:

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
    ^^^

Questions

Transform Function

for(int i = 1; i <= m; i++) {
    for(int j = 1; j <= n; j++) {
        if(c1[j - 1] == c2[i - 1]) dp[i][j] += dp[i - 1][j - 1] + dp[i][j - 1];
        else dp[i][j] += dp[i][j - 1];
    }
}

Solution

class Solution {
    public int numDistinct(String s, String t) {
        char[] c1 = s.toCharArray(), c2 = t.toCharArray();
        int n = c1.length, m = c2.length;
        int[][] dp = new int[m + 1][n + 1];
        Arrays.fill(dp[0], 1);

        for(int i = 1; i <= m; i++) {
            for(int j = 1; j <= n; j++) {
                if(c1[j - 1] == c2[i - 1]) dp[i][j] += dp[i - 1][j - 1];
                dp[i][j] += dp[i][j - 1];
            }
        }
        return dp[m][n];
    }
}