<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:
    def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
        # turn each string in the list into a tuple, with the num of ones and num of zeros
        self.str_counts = []

        for s in strs:
            zeros = s.count('0')
            ones = s.count('1')
            total = ones + zeros

            self.str_counts += [(total, zeros, ones)]

        self.str_counts.sort(reverse=True)

        # in typlical one, order them ascending, picking them as you go.
            # the subproblem is which one are you on, and what total weight you are aming to fill, what is the maximum 
            # amount of that you can utilize

        # this one, we want the most number of items, so have list asc, and for each weight, and remaning "weight", 
            # how many items can you get

        # how can we order these items if there are two weights?
            # by combined weight

        

        #dynamic problem, what information can we resuse in other search paths?

            # the 

        return self.helper((m, n), 0)

    @cache
    def helper(self, weight, ind):
        if ind >= len(self.str_counts):
            return 0
        
        # either choose the next item, or not, then get the maximum
        if weight[0] - self.str_counts[ind][1] >= 0 and weight[1] - self.str_counts[ind][2] >= 0:
            return max(self.helper((weight[0] - self.str_counts[ind][1], weight[1] - self.str_counts[ind][2]), ind + 1) + 1, self.helper(weight, ind + 1))
        else:
            return self.helper(weight, ind + 1)
        
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