reaching-points.py

# Time:  O(log(max(m, n)))
# Space: O(1)

# 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].

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

        return False