<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 = sum(nums)
        if total_sum % 2 == 1:
            return False
        else:
            target = int(total_sum / 2)
        nums.sort()
        # dp: dp[i][target] = answer for the question: 
        # are there any subset of [num_0,..., num_i] whose sum == target
        dp: list[dict] = []
        for i in range(len(nums)): 
            dp.append({0: True})
        def helper(ind: int, target_: int) -> bool:
            # are there any subset of [num_0,..., num_ind] whose sum == target
            if target_ < 0:      
                return False
            if target_ == 0:
                return True
            if ind == 0:
                if target_ == nums[0]:
                    dp[0][target_] = True
                    return True
                else: 
                    dp[0][target_] = False
                    return False
            # look up
            ans = dp[ind - 1][target_]
            if target_ >= nums[i]:
                ans = ans or dp[ind - 1][target_ - nums[i]]
            dp[ind][target_] = ans
            return ans
        
        for i in range(len(nums)):
            for t in range(target+1):
                helper(i, t)
        return dp[-1][target]
        
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