<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:

    struct Cache{
        std::vector<int> values;
        int width;
    };

    int getId(int lastElement, int maxValue, const Cache &cache){
        //return lastElement + cache.width * maxValue;
        return cache.width * lastElement + maxValue;
    }

    bool canPartition(vector<int>& nums) {
        
        auto sum = std::accumulate(nums.begin(), nums.end(), 0);
        if(sum % 2)
            return false;
        auto objective = sum / 2;

        Cache cache;
        cache.values = std::vector<int>(nums.size() * (objective + 1));
        //cache.width = nums.size();
        cache.width = (objective + 1);
        
        for (int lastElementAllowed = 0; lastElementAllowed < nums.size(); ++lastElementAllowed){
            for (int maxSumAllowed = 0; maxSumAllowed <= objective; ++maxSumAllowed){
                auto currentIndex = getId(lastElementAllowed, maxSumAllowed, cache);
                if (nums[lastElementAllowed] > maxSumAllowed){
                    if(lastElementAllowed == 0){
                        cache.values[currentIndex] = 0;
                        continue;
                    }
                    cache.values[currentIndex] = cache.values[getId(lastElementAllowed - 1, maxSumAllowed, cache)];
                    continue;
                }
                if(lastElementAllowed == 0){
                    cache.values[currentIndex] = nums[lastElementAllowed];
                    continue;
                }
                auto candidate1 = cache.values[getId(lastElementAllowed - 1, maxSumAllowed, cache)];
                auto candidate2 = cache.values[getId(lastElementAllowed - 1, maxSumAllowed - nums[lastElementAllowed], cache)] + nums[lastElementAllowed];
                cache.values[currentIndex] = std::max(candidate1, candidate2);
            }
        }

        return cache.values[getId(nums.size() - 1, objective, cache)] == objective;

        //return getMaxImpl(nums.size() - 1, objective, nums, cache) == objective;
    }
};
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