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.
rabbbitrabbbitrabbbit
Example 2:
Input: s = "babgbag", t = "bag"
Output: 5
Explanation:
As shown below, there are 5 ways you can generate "bag" from S.
babgbagbabgbagbabgbagbabgbagbabgbag
Distinct Subsequences - LeetCode
Let's first define its state dp[i][j] to be the number of distinct subsequences of t[0..i - 1] in s[0..j - 1]. Then we have the following state equations:
dp[i][j] = dp[i][j - 1] if t[i - 1] != s[j - 1];dp[i][j] = dp[i][j - 1] + dp[i - 1][j - 1] if t[i - 1] == s[j - 1];dp[0][j] = 1 for all j;dp[i][0] = 0 for all positive i.Now let's give brief explanations to the four equations above.
t[i - 1] != s[j - 1], the distinct subsequences will not include s[j - 1] and thus all the number of distinct subsequences will simply be those in s[0..j - 2], which corresponds to dp[i][j - 1];t[i - 1] == s[j - 1], the number of distinct subsequences include two parts: those with s[j - 1] and those without;