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Grokking the Coding Interview Patterns

Solution: Erect the Fence

Explore how to compute the convex hull of points to enclose trees with minimal fencing. Learn the Monotone Chain algorithm step-by-step, including sorting points, constructing lower and upper hulls using orientation checks, and combining results. Understand how this approach solves the fence perimeter problem and analyze its time and space complexity.

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Statement

You are given an array of points, trees, where trees[i] = [xᵢ, yᵢ] represents the location of a tree on a 2D plane. Your goal is to enclose all the trees using the shortest possible length of rope, forming a fence around the garden. A garden is considered well-fenced if every tree lies inside or on the boundary of the fence (i.e., the fence forms the convex hullThis is the smallest convex shape, completely encloses a set of points. of all the points).

Return the coordinates of the trees that lie exactly on the fence perimeter. You can return the answer in any order.

Constraints:

  • 1≤1 \leq trees.length ≤300\leq 300

  • trees[i].length == 22

  • 0≤0 \leq xi, yi ≤100\leq ...