<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:
        k = (n + 1) * (m + 1)
        dp = [ [0 for i in range(k)] for _ in range(len(strs)+1)]

        @lru_cache
        def getIndex(i, j):
            return (i * (n+1)) + j

        @lru_cache
        def getCord(i):
            return (i // (n+1), (i % (n+1)))
        # a = []
        for i in range(len(strs)):
            m1,n1 = 0,0
            for s in strs[i]:
                if s == '0':
                    m1 += 1
                else:
                    n1 += 1
            # a.append((m1,n1))
            
            for j in range(k):
                m2,n2 = getCord(j)
                if m2 < m1 or n2 < n1:
                    dp[i+1][j] = dp[i][j]
                    continue
                t = getIndex(m2-m1, n2-n1)
                dp[i+1][j] = max(dp[i][j], 1 + dp[i][t])
        # print(a)
        # for i in range(k):
        #     print(str(getCord(i)[0])+""+str(getCord(i)[1]),end = ",")
        # print()
        # for i in dp:
        #     print(i)
        return dp[-1][-1]
47631