<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>

from collections import defaultdict

# class Solution:
#     def canPartition(self, nums: List[int]) -> bool:
#         total_sum = sum(nums)
#         if total_sum % 2 != 0: return False
#         partition_sum = total_sum / 2
#         dp = dict()
#         return self.solve(len(nums) - 1, partition_sum, nums, dp)
    
#     def solve(self, i, target, nums, dp):
#         if target == 0: return True
#         if i == 0: return nums[0] == target
#         if (i, target) in dp: return dp[(i, target)]
#         not_take = self.solve(i-1, target, nums, dp)
#         take = self.solve(i-1, target-nums[i], nums, dp) if target > nums[i] else False
#         dp[(i, target)] = take or not_take
#         return dp[(i, target)]

class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        total_sum = sum(nums)
        if total_sum % 2 != 0: return False
        partition_sum = total_sum // 2
        return self.solve(partition_sum, nums)
        
    def solve(self, target, nums):
        dp = defaultdict(bool)
        n = len(nums)
        for i in range(n):
            dp[(i, 0)] = True
        dp[(0, nums[0])] = True
        
        for i in range(n):
            for j in range(1, target+1):
                not_take = dp[(i-1, j)]
                take = dp[(i-1, j-nums[i])] if j >= nums[i] else False
                dp[(i, j)] = take or not_take
        return dp[(n-1, target)]
                
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