Sync LeetCode submission Runtime - 479 ms (76.27%), Memory - 71.8 MB (22.76%)

Author: jimit105

0416-partition-equal-subset-sum/README.md

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+<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>

0416-partition-equal-subset-sum/solution.py

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+# Approach 2: Top Down Dynamic Programming - Memoization
+
+# n = len(nums), m = subset_sum
+# Time: O(m * n)
+# Space: O(m * n)
+
+class Solution:
+    def canPartition(self, nums: List[int]) -> bool:
+        @lru_cache(maxsize = None)
+        def dfs(nums, n, subset_sum):
+            if subset_sum == 0:
+                return True
+            if n == 0 or subset_sum < 0:
+                return False
+            result = (dfs(nums, n - 1, subset_sum - nums[n - 1]) or 
+                    dfs(nums, n - 1, subset_sum))
+            return result
+
+        total_sum = sum(nums)
+        if total_sum % 2 != 0:
+            return False
+
+        subset_sum = total_sum // 2
+        n = len(nums)
+        return dfs(tuple(nums), n - 1, subset_sum)