<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 TB(int i, int l, int r,vector<int>&rods, vector<vector<int>>&dp, int N)
    // {
    //     if(i==rods.size())
    //     {
            
    //         if(l-r==0)
    //         {
    //             cout<<l<<";";
    //             return l;
    //         }
    //         return 0;
    //     }

    //     int diff=l-r+N;
    //     if(dp[i][diff]!=-1) return dp[i][diff];
    //     int op1=TB(i+1,l,r,rods,dp,N);
    //     int op2=rods[i] + TB(i+1,l+rods[i],r,rods,dp,N);
    //     int op3=TB(i+1,l,r+rods[i],rods,dp,N);
    //     return dp[i][diff]=max(op1,max(op2,op3));
    // }
    int TB(int i, int diff,vector<int>&rods, vector<vector<int>>&dp, int N)
    {
        if(i==rods.size())
        {
            
            if(diff==0)
            {
                // cout<<l<<";";
                return 0;
            }
            return INT_MIN;
        }

        // int diff=l-r+N;
        if(dp[i][diff + N]!=-1) return dp[i][diff + N];
        int op1=TB(i+1,diff,rods,dp,N);
        int op2=rods[i] + TB(i+1,diff+rods[i],rods,dp,N);
        int op3=TB(i+1,diff - rods[i],rods,dp,N);
        return dp[i][diff + N] = max(op1,max(op2,op3));
    }
    int tallestBillboard(vector<int>& rods) {
        int n=rods.size();
        int N=accumulate(rods.begin(),rods.end(),0);
        vector<vector<int>>dp(n+1,vector<int>(2*N+1,-1));
        int res = TB(0,0,rods,dp,N);
        if(res<=0) return 0;
        return res;
    }
};
48721