<p>Given an integer array <code>nums</code>, return <code>true</code> <em>if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,5,11,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> The array can be partitioned as [1, 5, 5] and [11].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,5]
<strong>Output:</strong> false
<strong>Explanation:</strong> The array cannot be partitioned into equal sum subsets.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
</ul>

class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        total = sum(nums)
        if total % 2 == 1:
            return False
        
        target = total // 2
        nums = sorted(nums)
        if nums[-1] > target:
            return False

        dp = {}

        def try_fill(s, n):
            # print((s, n), dp)
            result = dp.get((s, n))
            if result is not None:
                return result
            
            def cache(result):
                dp[(s, n)] = result
                return result
            
            if n == 1:
                if s == nums[0]:
                    return cache(True)
                else:
                    return cache(False)
            else:
                if nums[n - 1] < s:
                    result = try_fill(s - nums[n - 1], n - 1)
                    if result:
                        return cache(result)
                result = try_fill(s, n - 1)
                return cache(result)
        
        return try_fill(target, len(nums))                

78714