<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 solve(vector<pair<int,int>>&nums, int num0, int num1, int index, vector<vector<vector<int>>> &dp) {
        if(index == nums.size() || (num0 == 0 && num1 == 0)) {
            return 0;
        }

        if(dp[num0][num1][index] != -1) {
            return dp[num0][num1][index];
        }

        if(nums[index].first > num0 || nums[index].second > num1) {
            return solve(nums,num0,num1,index+1,dp);
        }        

        int include = 1 + solve(nums, num0-nums[index].first, num1-nums[index].second, index+1,dp);
        int exclude = solve(nums,num0,num1,index+1,dp);

        return dp[num0][num1][index] = max(include,exclude);
    }
public:
    int findMaxForm(vector<string>& strs, int m, int n) {
        vector<pair<int,int>> nums;
        vector<vector<vector<int>>> dp(m+1,vector<vector<int>>(n+1,vector<int>(strs.size(),-1)));
        for(auto i : strs) {
            int num1 = 0, num0 = 0;

            for(auto ch : i) {
                (ch == '0') ? num0++ : num1++;
            }

            nums.push_back({num0,num1});
        }

        return solve(nums,m,n,0,dp);
    }
};
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