<p>Given two strings s and t, return <i>the number of distinct</i> <b><i>subsequences</i></b><i> of </i>s<i> which equals </i>t.</p>

<p>The test cases are generated so that the answer fits on a 32-bit signed integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;rabbbit&quot;, t = &quot;rabbit&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
As shown below, there are 3 ways you can generate &quot;rabbit&quot; from s.
<code><strong><u>rabb</u></strong>b<strong><u>it</u></strong></code>
<code><strong><u>ra</u></strong>b<strong><u>bbit</u></strong></code>
<code><strong><u>rab</u></strong>b<strong><u>bit</u></strong></code>
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;babgbag&quot;, t = &quot;bag&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong>
As shown below, there are 5 ways you can generate &quot;bag&quot; from s.
<code><strong><u>ba</u></strong>b<u><strong>g</strong></u>bag</code>
<code><strong><u>ba</u></strong>bgba<strong><u>g</u></strong></code>
<code><u><strong>b</strong></u>abgb<strong><u>ag</u></strong></code>
<code>ba<u><strong>b</strong></u>gb<u><strong>ag</strong></u></code>
<code>babg<strong><u>bag</u></strong></code></pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length, t.length &lt;= 1000</code></li>
	<li><code>s</code> and <code>t</code> consist of English letters.</li>
</ul>

class Solution {
public:
    int numDistinct(string s, string t) {
        int strLen = s.size();      // 2
        int targetLen = t.size();   // 5
        
        // std::vector<std::vector<int>> matrix(strLen + 1, std::vector<int>(targetLen + 1, -1));    
        std::vector<int> matrix(strLen * targetLen, -1);

        std::function<int(int,int)> dfs = [&](int i, int j) -> int {
            if(j == targetLen) {
                return 1;
            }
            if(i == strLen) {
                return 0;
            }
            
            // std::cout << i * targetLen + j << "\n";

            if(matrix[i * targetLen + j] >= 0) {
                return matrix[i * targetLen + j];
            }

            if (s[i] == t[j]) {
                matrix[i * targetLen + j] = dfs(i + 1, j + 1) + dfs(i + 1, j);
            } else {
                matrix[i * targetLen + j] = dfs(i + 1, j);
            }

            return matrix[i * targetLen + j];
        };

        return dfs(0, 0);
    }

};
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