<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:
        if sum(nums) % 2 == 1:
            return False
        target = sum(nums) // 2
        # mp = {}
        memo = [[-1] * (target + 1) for _ in range(len(nums))]
        def dp(remain, idx):
            if remain == 0:
                return True
            if idx >= len(nums) or remain < 0:
                return False
            # if (idx, remain) in mp:
            #     return mp[(idx, remain)]
            if memo[idx][remain] != -1:
                return memo[idx][remain]

            res_1 = dp(remain - nums[idx], idx + 1)
            res_2 = dp(remain, idx + 1)
            # mp[(idx, remain)] = res_1 or res_2
            memo[idx][remain] = res_1 or res_2
            return memo[idx][remain]
        return dp(target, 0)



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