Determine if a Cell Is Reachable at a Given Time — LeetCode 2849 Python Solution

The problem

You are given four integers sx, sy, fx, fy, and a non-negative integer t. In an infinite 2D grid, you start at the cell (sx, sy).

Example

Input

sx = 2, sy = 4, fx = 7, fy = 7, t = 6

Output

true

Explanation

Starting at cell (2, 4), we can reach cell (7, 7) in exactly 6 seconds by going through the cells depicted in the picture above.

Python solution

class Solution:
    def isReachableAtTime(self, sx: int, sy: int, fx: int, fy: int, t: int) -> bool:
        if sx == fx and sy == fy:
            return t != 1
        dx = abs(sx - fx)
        dy = abs(sy - fy)
        return max(dx, dy) <= t

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2849. Determine if a Cell Is Reachable at a Given Time is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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