<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 {
    int height(int i,int j,vector<int>& rods,unordered_map<int,unordered_map<int,int>>& mp){
        int n=rods.size();
        if(i==n){
            if(j==0)return 0;
            return INT_MIN;
        }
        if(mp[i].find(j)!=mp[i].end())return mp[i][j];
        int ans=INT_MIN;
        ans=height(i+1,j,rods,mp);
        ans=max(ans,rods[i]+height(i+1,j+rods[i],rods,mp));
        ans=max(ans,height(i+1,j-rods[i],rods,mp));
        return mp[i][j]=ans;
    }
public:
    int tallestBillboard(vector<int>& rods) {
        unordered_map<int,unordered_map<int,int>>mp;
        return height(0,0,rods,mp);
    }
};
168346