115. Distinct Subsequences

📋 Đề Bài

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.

🧠 Thuật Toán & Kỹ Thuật

Dynamic Programming (Quy hoạch động)Bit Manipulation (Thao tác bit)Matrix (Ma trận)String (Chuỗi)
⏱️ Thời gian O(n×m)
💾 Không gian O(n×m)

💻 Lời Giải

C++ 0115-distinct-subsequences.cpp
class Solution {
public:
    int numDistinct(string s, string t) {
        int n = s.size(), m = t.size();
        
        vector<vector<unsigned int>> dp(n + 1, vector<unsigned int>(m + 1));
        
        for (int i = 0; i <= n; ++i) {
            dp[i][0] = 1;
        }
        
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= m; ++j) {
                dp[i][j] = dp[i - 1][j];
                if (s[i - 1] == t[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
                }
            }
        }
        
        return dp[n][m];
    }
};