<p>You are given an array of binary strings <code>strs</code> and two integers <code>m</code> and <code>n</code>.</p>

<p>Return <em>the size of the largest subset of <code>strs</code> such that there are <strong>at most</strong> </em><code>m</code><em> </em><code>0</code><em>&#39;s and </em><code>n</code><em> </em><code>1</code><em>&#39;s in the subset</em>.</p>

<p>A set <code>x</code> is a <strong>subset</strong> of a set <code>y</code> if all elements of <code>x</code> are also elements of <code>y</code>.</p>

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

<pre>
<strong>Input:</strong> strs = [&quot;10&quot;,&quot;0001&quot;,&quot;111001&quot;,&quot;1&quot;,&quot;0&quot;], m = 5, n = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The largest subset with at most 5 0&#39;s and 3 1&#39;s is {&quot;10&quot;, &quot;0001&quot;, &quot;1&quot;, &quot;0&quot;}, so the answer is 4.
Other valid but smaller subsets include {&quot;0001&quot;, &quot;1&quot;} and {&quot;10&quot;, &quot;1&quot;, &quot;0&quot;}.
{&quot;111001&quot;} is an invalid subset because it contains 4 1&#39;s, greater than the maximum of 3.
</pre>

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

<pre>
<strong>Input:</strong> strs = [&quot;10&quot;,&quot;0&quot;,&quot;1&quot;], m = 1, n = 1
<strong>Output:</strong> 2
<b>Explanation:</b> The largest subset is {&quot;0&quot;, &quot;1&quot;}, so the answer is 2.
</pre>

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

<ul>
	<li><code>1 &lt;= strs.length &lt;= 600</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 100</code></li>
	<li><code>strs[i]</code> consists only of digits <code>&#39;0&#39;</code> and <code>&#39;1&#39;</code>.</li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
</ul>

class Solution {
public:
    int findMaxForm(vector<string>& strs, int m, int n) {
        vector<vector<vector<int>>> v(m + 1, vector<vector<int>>(n + 1, vector<int>(strs.size(), -1)));
        vector<int> z;
        vector<int> o;
        for (auto& s : strs){
            int oneC = 0, zeroC = 0;
            for (auto& c : s)
                if (c == '1') ++oneC;
                else ++zeroC;
            z.push_back(zeroC);
            o.push_back(oneC);
        }
        return dfs(v, z, o, m, n, 0);
    }
    int dfs(vector<vector<vector<int>>>& v, vector<int>& z, vector<int>& o, int m, int n, int ind){
        if (ind == z.size()) return 0;
        if (v[m][n][ind] != -1) return v[m][n][ind];
        return v[m][n][ind] = z[ind] <= m && o[ind] <= n ?
            max(1 + dfs(v, z, o, m - z[ind], n - o[ind], ind + 1), dfs(v, z, o, m, n, ind + 1)) :
            dfs(v, z, o, m, n, ind + 1);
    }
};
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