<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:
    vector<vector<vector<int>>> dp;
    int help(vector<pair<int, int>>& a, int i, int one, int zero, int m,
             int n) {
        if (one > n || zero > m)
            return INT_MIN;
        if (i == a.size())
            return 0;

        if (dp[i][one][zero] != -1)
            return dp[i][one][zero];

        int skip = help(a, i + 1, one, zero, m, n);
        int take = 0;

        take = 1 + help(a, i + 1, one + a[i].second, zero + a[i].first, m, n);

        return dp[i][one][zero] = max(take, skip);
    }
    int findMaxForm(vector<string>& v, int m, int n) {

        dp.resize(v.size(), vector<vector<int>>(n + 1, vector<int>(m + 1, -1)));

        // {zero,one}
        vector<pair<int, int>> a;
        for (auto i : v) {
            int x = i.size();
            int one = 0;
            for (auto c : i) {
                if (c == '1')
                    ++one;
            }
            a.push_back({x - one, one});
        }

        return help(a, 0, 0, 0, m, n);
    }
};
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