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Problem solution · Python

Erect the Fence II

Erect the Fence II: a Python solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
98 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Erect the Fence II, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 98 lines of Python from the credited upstream file 1924.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeErect the Fence II · PythonPython
Use this to learn the idea, then write your own version.
from dataclasses import dataclass  @dataclass(frozen=True)class Point:  x: float  y: float  @dataclass(frozen=True)class Disk:  center: Point  radius: float  class Solution:  def outerTrees(self, trees: list[list[int]]) -> list[float]:    points = [Point(x, y) for x, y in trees]    disk = self._welzl(points, 0, [])    return [disk.center.x, disk.center.y, disk.radius]   def _welzl(      self,      points: list[Point],      i: int,      planePoints: list[Point],  ) -> Disk:    """Returns the smallest disk that encloses points[i..n).     https://en.wikipedia.org/wiki/Smallest-disk_problem#Welzl's_algorithm    """    if i == len(points) or len(planePoints) == 3:      return self._trivial(planePoints)    disk = self._welzl(points, i + 1, planePoints)    if self._inside(disk, points[i]):      return disk    return self._welzl(points, i + 1, planePoints + [points[i]])   def _trivial(self, planePoints: list[Point]) -> Disk:    """Returns the smallest disk that encloses `planePoints`."""    if len(planePoints) == 0:      return Disk(Point(0, 0), 0)    if len(planePoints) == 1:      return Disk(Point(planePoints[0].x, planePoints[0].y), 0)    if len(planePoints) == 2:      return self._getDisk(planePoints[0], planePoints[1])     disk01 = self._getDisk(planePoints[0], planePoints[1])    if self._inside(disk01, planePoints[2]):      return disk01     disk02 = self._getDisk(planePoints[0], planePoints[2])    if self._inside(disk02, planePoints[1]):      return disk02     disk12 = self._getDisk(planePoints[1], planePoints[2])    if self._inside(disk12, planePoints[0]):      return disk12     return self._getDiskFromThree(        planePoints[0],        planePoints[1],        planePoints[2])   def _getDisk(self, A: Point, B: Point) -> Disk:    """Returns the smallest disk that encloses the points A and B."""    x = (A.x + B.x) / 2    y = (A.y + B.y) / 2    return Disk(Point(x, y), self._distance(A, B) / 2)   def _getDiskFromThree(self, A: Point, B: Point, C: Point) -> Disk:    """Returns the smallest disk that encloses the points A, B, and C."""    # Calculate midpoints.    mAB = Point((A.x + B.x) / 2, (A.y + B.y) / 2)    mBC = Point((B.x + C.x) / 2, (B.y + C.y) / 2)     # Calculate the slopes and the perpendicular slopes.    slopeAB = math.inf if B.x == A.x else (B.y - A.y) / (B.x - A.x)    slopeBC = math.inf if C.x == B.x else (C.y - B.y) / (C.x - B.x)    perpSlopeAB = math.inf if slopeAB == 0 else -1 / slopeAB    perpSlopeBC = math.inf if slopeBC == 0 else -1 / slopeBC     # Calculate the center.    x = (perpSlopeBC * mBC.x - perpSlopeAB * mAB.x +         mAB.y - mBC.y) / (perpSlopeBC - perpSlopeAB)    y = perpSlopeAB * (x - mAB.x) + mAB.y    center = Point(x, y)    return Disk(center, self._distance(center, A))   def _inside(self, disk: Disk, point: Point) -> bool:    """Returns True if the point is inside the disk."""    return disk.radius > 0 and self._distance(disk.center, point) <= disk.radius   def _distance(self, A: Point, B: Point) -> float:    dx = A.x - B.x    dy = A.y - B.y    return math.sqrt(dx**2 + dy**2)

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