Reaching Points — LeetCode 780 Python Solution

The problem

Given four integers sx, sy, tx, and ty, return true if it is possible to convert the point (sx, sy) to the point (tx, ty) through some operations, or false otherwise. The allowed operation on some point (x, y) is to convert it to either (x, x + y) or (x + y, y).

Example

Input

sx = 1, sy = 1, tx = 3, ty = 5

Output

true

Explanation

One series of moves that transforms the starting point to the target is:

Python solution

class Solution:
    def reachingPoints(self, sx: int, sy: int, tx: int, ty: int) -> bool:
        while tx > sx and ty > sy and tx != ty:
            if tx > ty:
                tx %= ty
            else:
                ty %= tx
        if tx == sx and ty == sy:
            return True
        if tx == sx:
            return ty > sy and (ty - sy) % tx == 0
        if ty == sy:
            return tx > sx and (tx - sx) % ty == 0
        return False

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 780. Reaching Points 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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