New Solution "Partition Equal Subset Sum"

README.md

@@ -13,6 +13,7 @@ LeetCode
 |643|[Maximum Average Subarray I](https://leetcode.com/problems/maximum-average-subarray-i/description/) | [C++](./algorithms/cpp/maximumAverageSubarray/MaximumAverageSubarray.I.cpp)|Easy|
 |477|[Total Hamming Distance](https://leetcode.com/problems/total-hamming-distance/) | [C++](./algorithms/cpp/totalHammingDistance/totalHammingDistance.cpp)|Medium|
 |418|[SentenceScreenFitting](https://leetcode.com/problems/sentence-screen-fitting/) ♥ | [C++](./algorithms/cpp/sentenceScreenFitting/sentenceScreenFitting.cpp)|Easy|
+|416|[Partition Equal Subset Sum](https://leetcode.com/problems/partition-equal-subset-sum/description/) | [C++](./algorithms/cpp/partitionEqualSubsetSum/PartitionEqualSubsetSum.cpp)|Medium|
 |415|[Add Strings](https://leetcode.com/problems/add-strings/) | [C++](./algorithms/cpp/addStrings/AddStrings.cpp)|Easy|
 |414|[Third Maximum Number](https://leetcode.com/problems/third-maximum-number/) | [C++](./algorithms/cpp/thirdMaximumNumber/ThirdMaximumNumber.cpp)|Easy|
 |413|[Arithmetic Slices](https://leetcode.com/problems/arithmetic-slices/) | [C++](./algorithms/cpp/arithmeticSlices/ArithmeticSlices.cpp)|Medium|

algorithms/cpp/partitionEqualSubsetSum/PartitionEqualSubsetSum.cpp

@@ -0,0 +1,65 @@
+// Source : https://leetcode.com/problems/partition-equal-subset-sum/description/
+// Author : Hao Chen
+// Date   : 2018-06-24
+
+/*************************************************************************************** 
+ *
+ * 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.
+ * 
+ * 
+ * Note:
+ * 
+ * Each of the array element will not exceed 100.
+ * The array size will not exceed 200.
+ * 
+ * 
+ * 
+ * Example 1:
+ * 
+ * Input: [1, 5, 11, 5]
+ * 
+ * Output: true
+ * 
+ * Explanation: The array can be partitioned as [1, 5, 5] and [11].
+ * 
+ * 
+ * 
+ * Example 2:
+ * 
+ * Input: [1, 2, 3, 5]
+ * 
+ * Output: false
+ * 
+ * Explanation: The array cannot be partitioned into equal sum subsets.
+ * 
+ ***************************************************************************************/
+
+class Solution {
+public:
+    //back tracking
+    bool canPartitionRecrusion(vector<int>& nums, int half, int index) {
+        for (int i=index; i<nums.size(); i++){
+            int h = half - nums[i];
+            if ( h < 0 ) return false; //cannot found the solution
+            if ( h == 0 ) return true; //found the solution
+            if ( canPartitionRecrusion(nums, h, i+1) == true ) return true;
+        }
+        return false;
+    }
+
+    
+    bool canPartition(vector<int>& nums) {
+        int sum = 0;
+        for(auto n : nums) sum +=n;
+        if ( sum & 1 ) return false; // sum % 2 !=  1
+        int half = sum / 2;
+        
+        //sort the array in descending order
+        //so, the DFS could be very fast to find the answer because it's greedy.
+        std::sort(nums.begin(), nums.end(), std::greater<int>()); 
+
+        //go to find a path which sum is half
+        return canPartitionRecrusion(nums, half, 0);
+    }
+};