human
I found an interesting problem on https://leetcode.com/problems/tallest-billboard/:
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.
You have a collection of rods which can be welded together.  For example, if you have rods of lengths 1, 2, and 3, you can weld them together to make a support of length 6.
Return the largest possible height of your billboard installation.  If you cannot support the billboard, return 0.
 
Example 1:
Input: [1,2,3,6]
Output: 6
Explanation: We have two disjoint subsets {1,2,3} and {6}, which have the same sum = 6.

Example 2:
Input: [1,2,3,4,5,6]
Output: 10
Explanation: We have two disjoint subsets {2,3,5} and {4,6}, which have the same sum = 10.


Example 3:
Input: [1,2]
Output: 0
Explanation: The billboard cannot be supported, so we return 0.

 
Note:

0 <= rods.length <= 20
1 <= rods[i] <= 1000
The sum of rods is at most 5000.

I tried it in Python, but could not do it. Can you solve it?

 Give me a the Python program you requested?
assistant
#Here is the Python program you requested.

class Solution:
    def tallestBillboard(self, rods: List[int]) -> int:
        # dp[diff] = a: have a pair of (a, a + diff)
        
        dp = {0: 0}
        for rod in rods:
            for d, x in list(dp.items()):
                dp[d + rod] = max(dp.get(d + rod, 0), x)
                dp[abs(d - rod)] = max(dp.get(abs(d - rod), 0), x + min(d, rod))
        
        return dp[0]