<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 {
private:
    int helper(vector<pair<int, int>>& data, int zeros, int ones, int idx){
        if(idx >= data.size() or (zeros == 0 and ones == 0)){
            return 0;
        }
        if(dp[idx][zeros][ones] != -1) return dp[idx][zeros][ones];
        if(data[idx].first > zeros or data[idx].second > ones ){
            return dp[idx][zeros][ones] = helper(data, zeros, ones, idx+1);
        }
        return dp[idx][zeros][ones] = max(1 + helper(data, zeros - data[idx].first, ones - data[idx].second, idx+1), helper(data, zeros , ones, idx+1));
    }
public:
    int8_t dp[601][101][101];
    int findMaxForm(vector<string>& strs, int m, int n) {
        memset(dp, -1, sizeof(dp));
        int zeros = m;
        int ones = n;
        vector<pair<int, int>> data;
        for( auto i : strs){
            int z = 0;
            int o = 0;
            for (auto j : i){
                j == '0' ? z++ : o++;
            }
            data.push_back({z, o});
        }
        return helper(data, zeros, ones, 0);
    }
};
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