<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 helper(int diff,vector<int>& rods,int i,   vector<vector<int>> &dp) {
        
        if(i>=rods.size()){
            if(diff==0)return dp[i][5000+diff]= 0;
            else return dp[i][5000+diff]=-1e9;
        }
        if(dp[i][5000+diff]!=-1)return dp[i][5000+diff];
       
        int choice1=rods[i]+helper(diff+rods[i],rods,i+1,dp);
        int choice2=rods[i]+helper(diff-rods[i],rods,i+1,dp);
        int choice3=helper(diff,rods,i+1,dp);
        return dp[i][5000+diff]=max(choice1,max(choice2,choice3));
    }
    int tallestBillboard(vector<int>& rods) {
        // int ans=helper(0,0,rods,0);
        // if(ans==INT_MIN)return 0;
        vector<vector<int>> dp(22,vector<int>(10003,-1));
        int n=rods.size();
        int ans=helper(0,rods,0,dp);
        if(ans==-1e9)return 0;
        return ans/2;


    }
};
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