Leetcode 115. Distinct Subsequences

Seawolf

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).

It's 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.
(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
    ^^^

1. class Solution:
   
2.     def numDistinct(self, s: str, t: str) -> int:
   
3.         m, n = len(s), len(t)
   
4.         dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
   
5.         
   
6.         for i in range(m + 1):
   
7.             for j in range(n + 1):
   
8.                
   
9.                 if j == 0:
   
10.                     dp[i][j] = 1
    
11.                     continue
    
12.                
    
13.                 if i == 0:
    
14.                     dp[i][j] = 0
    
15.                     continue
    
16.                
    
17.                 dp[i][j] = dp[i - 1][j]
    
18.                
    
19.                 if s[i - 1] == t[j - 1]:
    
20.                     dp[i][j] += dp[i - 1][j - 1]
    
21.         
    
22.         return dp[m][n]

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