<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 count(int i,char val,vector<string>& strs){
        int count = 0;

        for(int j = 0;j<strs[i].size();j++){
            if (strs[i][j]==val){
                count++;
            }
        }
        return count;
    }
    
    int rec(int i,int one,int zero,vector<string>& strs, int m, int n,vector<vector<vector<int>>> &dp){
        if (i>=strs.size()) return 0;

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

        int pick = 0;

        int x = count(i,'1',strs);
        int y = count(i,'0',strs);

        if (x+one<=n && y+zero<=m){
            pick = 1+rec(i+1,one+x,zero+y,strs,m,n,dp);
        }
        int not_pick = rec(i+1,one,zero,strs,m,n,dp);

        dp[i][one][zero]= max(pick,not_pick);
        return dp[i][one][zero];
    }

    int findMaxForm(vector<string>& strs, int m, int n) {
        int k = strs.size();
        vector<vector<vector<int>>> dp(k, vector<vector<int>>(n+1, vector<int>(m+1, -1)));

        return rec(0,0,0,strs,m,n,dp);
    }
};
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