<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>

# input : int array
# output: boolean

# partition equal sum
# which means can get subset sum = total // 2

# sort array
# recursion

# for each number we can choose to take it or not
#

class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        nums.sort()
        memo = {}
        def partition(start, target):
            if (start, target) in memo:
                return  memo[(start, target)]
            if start >= len(nums):
                return False
            if nums[start] == target:
                memo[(start, target)] = True
            elif nums[start] > target:
                memo[(start, target)] = False
            else:
                memo[(start, target)] = partition(start + 1, target) or partition(start+1, target-nums[start])
            return  memo[(start, target)]
        total = sum(nums)
        if total %2 ==1:
            return False
        return partition(0, total//2)
        
215650