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115. Distinct Subsequences

String Dynamic Programming

Problem - Distinct Subsequences

Hard

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

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

 

Constraints:

  • 1 <= s.length, t.length <= 1000
  • s and t consist of English letters.

Solutions

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class Solution:
    def numDistinct(self, s: str, t: str) -> int:
        m, n = len(s), len(t)
        dp = [[0] * (n + 1) for _ in range(m + 1)]

        for i in range(m + 1):
            dp[i][0] = 1

        for i, val1 in enumerate(s, 1):
            for j, val2 in enumerate(t, 1):
                dp[i][j] = dp[i - 1][j]
                if val1 == val2:
                    dp[i][j] += dp[i - 1][j - 1]

        return dp[-1][-1]

Submission Stats:

  • Runtime: 403 ms (68.96%)
  • Memory: 74.2 MB (47.36%)