115. Distinct Subsequences

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115. Distinct Subsequences

Description

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:

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Input: s = "rabbbit", t = "rabbit"
Output: 3

Explanation:
As shown below, there are 3 ways you can generate “rabbit” from s.

rabb b it

ra b bbit

rab b bit

Example 2:

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Input: s = "babgbag", t = "bag"
Output: 5

Explanation:
As shown below, there are 5 ways you can generate “bag” from s.

ba b g bag

ba bgba g

b abgb ag

ba b gb ag

babg bag

Constraints:

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

Hints/Notes

  • 2024/07/11
  • dp
  • No solution from 0x3F

Solution

Language: C++

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class Solution {
public:
    string s_, t_;
    vector<vector<int>> dp;

    int numDistinct(string s, string t) {
        dp.resize(s.size(), vector<int>(t.size(), -1));
        s_ = s;
        t_ = t;
        int res = traverse(0, 0);
        return res;
    }

    int traverse(int idx1, int idx2) {
        if (idx2 == t_.size()) {
            return 1;
        }
        if (idx1 == s_.size()) {
            return 0;
        }
        if (dp[idx1][idx2] != -1) {
            return dp[idx1][idx2];
        }
        int ans = 0;
        if (s_[idx1] == t_[idx2]) {
            ans += traverse(idx1 + 1, idx2 + 1);
        }
        ans += traverse(idx1 + 1, idx2);
        dp[idx1][idx2] = ans;
        return ans;
    }
};