<p>You are installing a billboard and want it to have the largest height. The billboard will have two steel supports, one on each side. Each steel support must be an equal height.</p>

<p>You are given a collection of <code>rods</code> that can be welded together. For example, if you have rods of lengths <code>1</code>, <code>2</code>, and <code>3</code>, you can weld them together to make a support of length <code>6</code>.</p>

<p>Return <em>the largest possible height of your billboard installation</em>. If you cannot support the billboard, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2,3,6]
<strong>Output:</strong> 6
<strong>Explanation:</strong> We have two disjoint subsets {1,2,3} and {6}, which have the same sum = 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2,3,4,5,6]
<strong>Output:</strong> 10
<strong>Explanation:</strong> We have two disjoint subsets {2,3,5} and {4,6}, which have the same sum = 10.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The billboard cannot be supported, so we return 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= rods.length &lt;= 20</code></li>
	<li><code>1 &lt;= rods[i] &lt;= 1000</code></li>
	<li><code>sum(rods[i]) &lt;= 5000</code></li>
</ul>

class Solution {
public:


    int tallestBillboard(vector<int>& rods) {

        int n = rods.size();
        unordered_map<int, int> map;
        map[0] = 0;
        for(int i = 0 ; i < n; i++) {
            unordered_map<int,int> newMap;
            for(auto& entry : map) {
                int diff = entry.first;
                int height = entry.second;

                //three possibility
                //1. add to taller side.
                newMap[diff + rods[i]] = max(newMap[diff + rods[i]], height + rods[i]);
                //2. do nothing.
                newMap[diff] = max(newMap[diff], height);
                //3. add to shorter side.
                int newShortSide = height - diff + rods[i];
                newMap[abs(height - newShortSide)] = max(newMap[abs(height - newShortSide)], max(height, newShortSide));
            }
            map = newMap;
        }

        

        return map[0];


    }
};
89503