Partition Equal Subset Sum

Author: BarthJr

partition_equal_subset_sum.py

@@ -0,0 +1,46 @@
+# https://www.lintcode.com/problem/partition-equal-subset-sum/description
+
+# Given a non-empty array 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:
+# Input: nums = [1, 5, 11, 5],
+# Output: true
+# Explanation:
+# two subsets: [1, 5, 5], [11]
+
+"""
+>>> Solution().canPartition([1, 5, 11, 5])
+True
+>>> Solution().canPartition([1, 2, 3, 9])
+False
+>>> Solution().canPartition([1, 4, 5, 6, 1, 32, 4, 1, 3, 4, 5, 5, 5, 5, 1, 2, 4, 5, 1])
+True
+"""
+
+
+class Solution:
+    """
+    @param nums: a non-empty array only positive integers
+    @return: true if can partition or false
+    """
+
+    def canPartition(self, nums):
+        memo = dict()
+        total = sum(nums)
+        if total % 2 != 0:
+            return False
+        return self._canPartition(nums, 0, 0, total, memo)
+
+    def _canPartition(self, nums, index, partial_sum, total, memo):
+        current = f'{index}_{partial_sum}'
+        if current in memo:
+            return memo[current]
+        if partial_sum * 2 == total:
+            return True
+        elif partial_sum > total // 2 or index >= len(nums):
+            return False
+        without_get_number = self._canPartition(nums, index + 1, partial_sum, total, memo)
+        get_number = self._canPartition(nums, index + 1, partial_sum + nums[index], total, memo)
+        memo[current] = without_get_number or get_number
+        return memo[current]