780. Reaching Points

A move consists of taking a point (x, y) and transforming it to either (x, x+y) or (x+y, y).

Given a starting point (sx, sy) and a target point (tx, ty), return True if and only if a sequence of moves exists to transform the point (sx, sy) to (tx, ty). Otherwise, return False.

Examples:
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:
(1, 1) -> (1, 2)
(1, 2) -> (3, 2)
(3, 2) -> (3, 5)

Input: sx = 1, sy = 1, tx = 2, ty = 2
Output: False

Input: sx = 1, sy = 1, tx = 1, ty = 1
Output: True

Note:

sx, sy, tx, ty will all be integers in the range [1, 10^9].

一刷
题解：首先找到tx和ty的最大公约数g，因为两个数a和b的最大公约数g可以表示为a和b的线性和。也就是说，存在整数s和t使g = sa + tb

用辗转相除法求得g

class Solution:
    def reachingPoints(self, sx, sy, tx, ty):
        """
        :type sx: int
        :type sy: int
        :type tx: int
        :type ty: int
        :rtype: bool
        """
        while sx < tx and sy < ty:#find common divisor
            if tx>ty: tx %=ty
            else: ty %= tx
        if sx == tx: return (ty-sy)%sx == 0
        if sy == ty return (tx -sx) %sy == 0
        return False