HardNo. 0956
Tallest Billboard — LeetCode 956 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Array, Dynamic Programming
- Reading time
- 2 min
- Source
- leetcode.com
The problem
You are installing a billboard and want it to have the largest height. The billboard will have two steel supports, one on each side.
Example
- Input
- rods = [1,2,3,6]
- Output
- 6
- Explanation
- We have two disjoint subsets {1,2,3} and {6}, which have the same sum = 6.
Python solution
class Solution:
def tallestBillboard(self, rods: List[int]) -> int:
@cache
def dfs(i: int, j: int) -> int:
if i >= len(rods):
return 0 if j == 0 else -inf
ans = max(dfs(i + 1, j), dfs(i + 1, j + rods[i]))
ans = max(ans, dfs(i + 1, abs(rods[i] - j)) + min(j, rods[i]))
return ans
return dfs(0, 0)Complexity
- Time
- O(n·m) (typical)
- Space · auxiliary
- O(n·m)or optimized
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 956. Tallest Billboard is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.
The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0960 | Delete Columns to Make Sorted III | Hard |
| 0045 | Jump Game II | Medium |
| 0053 | Maximum Subarray | Medium |
| 0055 | Jump Game | Medium |
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
Frequently asked questions
- How hard is LeetCode 956. Tallest Billboard?
LeetCode 956. Tallest Billboard is rated Hard on LeetCode.
- What topics does LeetCode 956. Tallest Billboard cover?
LeetCode 956. Tallest Billboard is tagged Array and Dynamic Programming on LeetCode.