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Path Existence with Constraints
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Path Existence with Constraints

HardPython

Problem

Does a path exist? Reach (x2, y2) from (x1, y1) using moves (x+y, y), (x, x+y), (x+c, y+c) without stepping on cells where x+y is a perfect square.

Asked in the Online assessment stage. The problem was shown as images; the poster summarized the function as canReach(c, x1, y1, x2, y2).

Implement canReach(c, x1, y1, x2, y2) and return a boolean. Coordinates and c are positive integers. A move may not exceed (x2, y2), and both the starting and target cells are forbidden when their coordinate sums are perfect squares.

Constraints

  • 1 <= c <= 100
  • 1 <= x1, y1, x2, y2 <= 100
  • The coordinates are integer cell positions
  • A path may use only cells with x <= x2 and y <= y2
  • The starting and target cells are also subject to the perfect-square restriction

Function Signature

def canReach(c, x1, y1, x2, y2):
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