<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:
    int n;
    unordered_map<string, bool> memo;
    bool canPartition(vector<int>& nums) { //main logic: a subset with a sum equal to half the sum of the entire array.
        n = nums.size();
        int sum = 0;
        for(int num : nums) {sum += num;}
        if (sum % 2 == 1) {return false;}
        int target = sum/2;
        return solve(nums, target, 0);
    }


    bool solve(vector<int>& nums, int target, int i)
    {
        if (target == 0) {return true;}
        if (i == n || target < 0 ) {return false;}

        string key = to_string(target) + '-' + to_string(i);
        if (memo.find(key) != memo.end()) {return memo[key];}

        int res = false;
        res = res || solve(nums, target - nums[i], i+1);
        res = res || solve(nums, target, i+1);
        memo[key] = res;
        return memo[key];
    }


};
216858