<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();
    //     if (n==1)return 0;
    //     if(n==2)return rods[0]==rods[1];
    //     int totSum=0;
    //     for(int i=0;i<n;i++)totSum+=rods[i];
    //     int target=totSum;
    //     vector<vector<bool>>dp(n,vector<bool>(target+1,false));
    //     for(int i=0;i<n;i++)dp[i][0]=true;
    //     if(rods[0]<target)dp[0][rods[0]]=true;
    //     for(int ind=1;ind<n;ind++){
    //         for(int tar=1;tar<=target;tar++){
    //             bool not_take = dp[ind-1][tar];
    //             bool take=false;
    //             if(tar-rods[ind]>=0)take=dp[ind-1][tar-rods[ind]];
    //             dp[ind][tar]= not_take || take ;
    //         }
    //     }
    //     if(target%2==1){
    //         if(dp[n-1][target/2]==true && dp[n-1][target-1]==true)return target/2;
    //         else return 0;
    //     }
    //     else{
    //         if(dp[n-1][target/2]==true)return target/2;
    //         else return 0;
    //     }
class Solution {
public:
    int tallestBillboard(vector<int>& rods) {
        unordered_map<int, int> dp;
        dp[0] = 0;
        for (int rod : rods) {
            unordered_map<int, int> temp;
            for (auto& [d, h] : dp) {
                temp[d] = max(temp[d], h);
                temp[d + rod] = max(temp[d + rod], h + rod);
                temp[d - rod] = max(temp[d - rod], h);
            }
            dp = temp;
        }
        return dp[0];
    }
};
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