<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:
        def nums(str):
            ones = sum(list(map(int, list(str))))
            return [len(str) - ones, ones]
        strs = [nums(str) for str in strs]
        dp = [[[0] * (n+1) for k in range(1+m)]   for l in range(len(strs))]
        for l, str in enumerate(strs):
            if l == 0:
                for k in range(m+1):
                    for i in range(n+1):
                        dp[l][k][i] = 1 if str[0] <= k  and str[1] <= i else 0
            else:
                for k in range(m+1):
                    for i in range(n+1):
                        if str[0] > k or str[1] > i:
                            dp[l][k][i] = dp[l-1][k][i]
                        else:
                            dp[l][k][i] = max(dp[l-1][k-str[0]][i-str[1]] + 1, dp[l-1][k][i])
        return dp[-1][m][n]

class Solution:
    def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
        counter=[[s.count("0"), s.count("1")] for s in strs]
        
        @cache
        def dp(i,j,idx):
            if i<0 or j<0:
                return -math.inf
            
            if idx==len(strs):
                return 0
            
            return max(dp(i,j,idx+1), 1 + dp(i-counter[idx][0], j-counter[idx][1], idx+1))
        return dp(m,n,0)
271043