<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>

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % 2 == 1)
            return false;
        int halfSum = sum/2;
        vector<vector<char>> memos(nums.size(), vector<char>(halfSum+1, -1));
        return dfs(nums, halfSum, 0, memos);
    }

    bool dfs(vector<int>& nums, int sum, int i, vector<vector<char>> & memos) {
        bool res = sum == 0;

        if (res || i == nums.size())
            return res;

        if (memos[i][sum] != -1)
            return memos[i][sum] == 1;

        if (!res && nums[i] <= sum)
            res = dfs(nums, sum - nums[i], i+1, memos);
        if (!res) {
            res = dfs(nums, sum, i+1, memos);
        }
        memos[i][sum] = res ? 1 : 0;
        return res;
    }
};
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