<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<string> strs;

int memo[601][202][202];
    int cnt(string& s) {
        int res = 0;
        for(int i = 0; i < s.size(); i++) {
            res += s[i] == '1';
        }
        return res;
    }
    int sol(int i, int m, int n) {
        if(i == strs.size() or (m == 0 and n == 0))   return 0;


        if(memo[i][m + 100][n + 100] != -1) 
            return memo[i][m + 100][n + 100];

        int cnt1s = cnt(strs[i]);
        int cnt0s = strs[i].size() - cnt1s;
        if(cnt1s > n or cnt0s > m)  
            return sol(i + 1, m, n);
        int take, skip;
        take = 1 + sol(i + 1, m - cnt0s, n - cnt1s);
        skip = sol(i + 1, m, n);

        return memo[i][m + 100][n + 100] = max(take, skip);
    }
    int findMaxForm(vector<string>& strs, int m, int n) {
        this->strs = strs;
        memset(memo, -1, sizeof(memo));
        return sol(0, m, n);
    }
};
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