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Problem solution · Python

Maximize the Distance Between Points on a Square

Maximize the Distance Between Points on a Square: a Python solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Breadth-first search
Source
walkccc LeetCode Solutions
Length
71 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

Breadth-first search

For Maximize the Distance Between Points on a Square, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 71 lines of Python from the credited upstream file 3464.py.
  • The implementation visibly relies on sequence storage, work queue.
  • No explicit loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

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 codeMaximize the Distance Between Points on a Square · PythonPython
Use this to learn the idea, then write your own version.
from dataclasses import dataclass  @dataclass(frozen=True)class Sequence:  startX: int  startY: int  endX: int  endY: int  length: int   def __iter__(self):    yield self.startX    yield self.startY    yield self.endX    yield self.endY    yield self.length  class Solution:  def maxDistance(self, side: int, points: list[list[int]], k: int) -> int:    ordered = self._getOrderedPoints(side, points)     def isValidDistance(m: int) -> bool:      """      Returns True if we can select `k` points such that the minimum Manhattan      distance between any two consecutive chosen points is at least `m`.      """      dq = collections.deque([Sequence(*ordered[0], *ordered[0], 1)])      maxLength = 1       for i in range(1, len(ordered)):        x, y = ordered[i]        startX, startY = ordered[i]        length = 1        while dq and abs(x - dq[0].endX) + abs(y - dq[0].endY) >= m:          if (abs(x - dq[0].startX) + abs(y - dq[0].startY) >= m                  and dq[0].length + 1 >= length):            startX = dq[0].startX            startY = dq[0].startY            length = dq[0].length + 1            maxLength = max(maxLength, length)          dq.popleft()        dq.append(Sequence(startX, startY, x, y, length))       return maxLength >= k     l = 0    r = side     while l < r:      m = (l + r + 1) // 2      if isValidDistance(m):        l = m      else:        r = m - 1     return l   def _getOrderedPoints(self, side: int, points: list[list[int]]) -> list[list[int]]:    """    Returns the ordered points on the perimeter of a square of side length    `side`, starting from left, top, right, and bottom boundaries.    """    left = sorted([(x, y) for x, y in points if x == 0 and y > 0])    top = sorted([(x, y) for x, y in points if x > 0 and y == side])    right = sorted([(x, y) for x, y in points if x == side and y < side],                   reverse=True)    bottom = sorted([(x, y) for x, y in points if y == 0], reverse=True)    return left + top + right + bottom

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