How do you solve Erect the Fence on LeetCode?

Erect the Fence (LeetCode #587) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Understanding the Convex Hull is crucial for solving perimeter problems efficiently.

What is the brute force solution for Erect the Fence?

The brute force approach for Erect the Fence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible combination of points to determine which trees can form the boundary of the fence. This method is straightforward but inefficient for larger datasets. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Erect the Fence?

Erect the Fence uses the following concepts: Array, Math, Geometry. The recommended patterns to study are: Convex Hull, Sorting.

What are the interview tips for Erect the Fence?

Always clarify the problem requirements and constraints before diving into the solution. Explain your thought process while coding to show your understanding. Practice implementing geometric algorithms, as they often appear in interviews.

What are common mistakes when solving Erect the Fence?

Failing to consider edge cases, such as collinear points. Not properly managing the stack during hull construction.

#587

Erect the Fence

Hard

ArrayMathGeometryConvex HullSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n)Space O(n)

The optimal approach uses the Convex Hull algorithm, which efficiently finds the smallest enclosing polygon for a set of points. This method significantly reduces the number of points we need to consider for the fence.

⚙️

Algorithm

4 steps

1Step 1: Sort the trees based on their x-coordinates (and y-coordinates for ties).
2Step 2: Build the lower hull by iterating through the sorted points and maintaining a stack of points that form the hull.
3Step 3: Build the upper hull by iterating through the sorted points in reverse order.
4Step 4: Combine the lower and upper hulls to get the complete fence.

solution.py21 lines

1# Full working Python code
2from typing import List
3
4def optimal_fence(trees: List[List[int]]) -> List[List[int]]:
5    def cross(o, a, b):
6        return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
7
8    trees = sorted(trees)
9    lower = []
10    for p in trees:
11        while len(lower) >= 2 and cross(lower[-2], lower[-1], p) < 0:
12            lower.pop()
13        lower.append(p)
14
15    upper = []
16    for p in reversed(trees):
17        while len(upper) >= 2 and cross(upper[-2], upper[-1], p) < 0:
18            upper.pop()
19        upper.append(p)
20
21    return lower[:-1] + upper[:-1]

ℹ

Complexity note: The time complexity is dominated by the sorting step, which is O(n log n), while the space complexity is O(n) due to the storage of the hull points.

1Understanding the Convex Hull is crucial for solving perimeter problems efficiently.
2Sorting points is often a necessary step in geometric algorithms.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.