Problem Description
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 are given a collection of rods that can be welded together. Return the largest possible height of your billboard installation. If you cannot support the billboard, return 0.
Key Insights
- The problem can be reduced to finding two subsets of rods that have equal sums, as these would represent the two supports of the billboard.
- Dynamic programming can be utilized to keep track of possible heights that can be achieved with different combinations of rods.
- The challenge lies in efficiently managing the height sums while ensuring both sides are equal.
Space and Time Complexity
Time Complexity: O(n * sum/2), where n is the number of rods and sum is the total length of the rods. Space Complexity: O(sum/2), for storing possible height differences.
Solution
The solution involves using a dynamic programming approach where we maintain a dictionary (or hash map) to track achievable height differences from the total sum of rods. We iterate through each rod and update the possible height differences. By ensuring that we balance the contributions to both sides, we can find the maximum height that can be achieved.