<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:
void re(int i,vector<int>rods,int n1,int n2,int &m){
    if(n1==n2){
        m=max(n1,n2);
    }
    if(i<0){
        return;
    }
    
    re(i-1,rods,n1,n2,m);
    re(i-1,rods,n1+rods[i],n2,m);
    re(i-1,rods,n1,n2+rods[i],m);


}
    int tallestBillboard(vector<int>& rods) {
        std::unordered_map<int, int> dp;
        dp[0] = 0;  // Base case: difference of 0 with height 0

        for (int rod : rods) {
            // Create a temporary copy of the current dp state
            std::unordered_map<int, int> dp_copy = dp;
            
            for (const auto& [diff, height] : dp) {
                // Case 1: Add the rod to one side
                dp_copy[diff + rod] = std::max(dp_copy[diff + rod], height);
                
                // Case 2: Add the rod to the other side
                dp_copy[std::abs(diff - rod)] = std::max(dp_copy[std::abs(diff - rod)], height + std::min(diff, rod));
            }
            
            // Update dp with the new values
            dp = std::move(dp_copy);
        }

        return dp[0];
    }
};
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