Given a non-empty array nums containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.
Example 1:
Input: nums = [1,5,11,5]
Output: true
Explanation: The array can be partitioned as [1, 5, 5] and [11].
Example 2:
Input: nums = [1,2,3,5]
Output: false
Explanation: The array cannot be partitioned into equal sum subsets.
Constraints:
-
1 <= nums.length <= 200 -
1 <= nums[i] <= 100
SOLUTION:
class Solution:
def isSubsetSum(self, arr, total, n):
if total == 0:
return True
if total != 0 and n == 0:
return False
if (n, total) in self.cache:
return self.cache[(n, total)]
if 2 * arr[n - 1] > total:
return self.isSubsetSum(arr, total, n - 1)
self.cache[(n, total)] = self.isSubsetSum(arr, total, n - 1) or self.isSubsetSum(arr, total - 2 * arr[n - 1], n - 1)
return self.cache[(n, total)]
def canPartition(self, nums: List[int]) -> bool:
self.cache = {}
n = len(nums)
total = sum(nums)
if total % 2 == 1:
return False
return self.isSubsetSum(nums, total, n)
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