add: partition-equal-subset-sum

Author: maxyzli

README.md

@@ -1,6 +1,6 @@
 # LeetCode
 
-![](https://img.shields.io/badge/solved-225-337ab7?style=for-the-badge&logo=appveyor.svg) 
+![](https://img.shields.io/badge/solved-226-337ab7?style=for-the-badge&logo=appveyor.svg) 
 ![](https://img.shields.io/badge/language-Java-yellow?style=for-the-badge&logo=appveyor.svg)
 
 LeetCode Solution in Java
@@ -379,6 +379,7 @@ LeetCode Solution in Java
 |322|[Coin Change (Classic)](https://leetcode.com/problems/coin-change/)|[Java](dynamic-programming/coin-change/README.md)|Medium|
 |343|[Integer Break](https://leetcode.com/problems/integer-break/)|[Java](dynamic-programming/integer-break/README.md)|Medium|
 |368|[Largest Divisible Subset](https://leetcode.com/problems/largest-divisible-subset/)|[Java](dynamic-programming/largest-divisible-subset/README.md)|Medium|
+|416|[Partition Equal Subset Sum (Classic)](https://leetcode.com/problems/partition-equal-subset-sum/)|[Java](dynamic-programming/partition-equal-subset-sum/README.md)|Medium|
 |486|[Predict the Winner (Classic)](https://leetcode.com/problems/predict-the-winner/)|[Java](dynamic-programming/predict-the-winner/README.md)|Medium|
 |516|[Longest Palindromic Subsequence (Classic)](https://leetcode.com/problems/longest-palindromic-subsequence/)|[Java](dynamic-programming/longest-palindromic-subsequence/README.md)|Medium|
 |518|[Coin Change 2 (Classic)](https://leetcode.com/problems/coin-change-2/)|[Java](dynamic-programming/coin-change-2/README.md)|Medium|

dynamic-programming/partition-equal-subset-sum/README.md

@@ -0,0 +1,86 @@
+# Partition Equal Subset Sum
+
+## Solution 1
+
+DFS
+
+```java
+/**
+ * Question   : 416. Partition Equal Subset Sum
+ * Complexity : Time: O(2^n) ; Space: O(n)
+ * Topics     : DP
+ */
+class Solution {
+    public boolean canPartition(int[] nums) {
+        int totalSum = 0;
+        for (int num : nums) {
+            totalSum += num;
+        }
+        
+        if (totalSum % 2 != 0) {
+            return false;
+        }
+        
+        return canPartitionUtil(nums, totalSum / 2, nums.length);
+    }
+
+    private boolean canPartitionUtil(int[] nums, int sum, int n) {
+        if (sum == 0) {
+            return true;
+        }
+        if (sum < 0 || n == 0) {
+            return false;
+        }
+
+        if (nums[n - 1] > sum) {
+            return canPartitionUtil(nums, sum, n - 1);
+        }
+        return canPartitionUtil(nums, sum - nums[n - 1], n - 1) || canPartitionUtil(nums, sum, n - 1); 
+    }
+}
+```
+
+## Solution 2
+
+DP
+
+```java
+/**
+ * Question   : 416. Partition Equal Subset Sum
+ * Complexity : Time: O(n * amount) ; Space: O(n * amount)
+ * Topics     : DP
+ */
+class Solution {
+    public boolean canPartition(int[] nums) {
+        int totalSum = 0;
+        for (int num : nums) {
+            totalSum += num;
+        }
+
+        if (totalSum % 2 != 0) {
+            return false;
+        }
+
+        int sum = totalSum / 2;
+        int n = nums.length;
+
+        // dp[i][j]: if we can generate j amount using i numbers.
+        boolean[][] dp = new boolean[n + 1][sum + 1];
+        for (int i = 0; i <= n; i++) {
+            dp[i][0] = true;
+        }
+
+        for (int i = 1; i <= n; i++) {
+            for (int currSum = 1; currSum <= sum; currSum++) {
+                if (currSum >= nums[i - 1]) {
+                    dp[i][currSum] = dp[i - 1][currSum] || dp[i - 1][currSum - nums[i - 1]];
+                } else {
+                    dp[i][currSum] = dp[i - 1][currSum];
+                }
+            }
+        }
+
+        return dp[n][sum];
+    }
+}
+```