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].

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从点 (x, y) 可以转换到 (x, x+y)  或者 (x+y, y)。

给定一个起点 (sx, sy) 和一个终点 (tx, ty)，如果通过一系列的转换可以从起点到达终点，则返回 True ，否则返回 False。

示例:
输入: sx = 1, sy = 1, tx = 3, ty = 5
输出: True
解释:
可以通过以下一系列转换从起点转换到终点：
(1, 1) -> (1, 2)
(1, 2) -> (3, 2)
(3, 2) -> (3, 5)

输入: sx = 1, sy = 1, tx = 2, ty = 2
输出: False

输入: sx = 1, sy = 1, tx = 1, ty = 1
输出: True

注意:

• sx, sy, tx, ty 是范围在 [1, 10^9] 的整数。

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Runtime: 4 ms Memory Usage: 18.4 MB

1 class Solution {
2     func reachingPoints(_ sx: Int, _ sy: Int, _ tx: Int, _ ty: Int) -> Bool { 
3         if tx < sx || ty < sy {return false}
4         if tx == sx && (ty - sy) % sx == 0 {return true}
5         if ty == sy && (tx - sx) % sy == 0 {return true}
6         return reachingPoints(sx, sy, tx % ty, ty % tx)        
7     }
8 }

---

4ms

 1 class Solution {
 2     func reachingPoints(_ sx: Int, _ sy: Int, _ tx: Int, _ ty: Int) -> Bool {
 3         var tx = tx, ty = ty
 4         while tx >= sx && ty >= sy {
 5             if tx == ty {break}
 6             if tx > ty {
 7                 if ty > sy {
 8                     tx %= ty
 9                 } else {
10                     return (tx - sx) % ty == 0
11                 }
12             } else {
13                 if (tx > sx) {
14                     ty %= tx
15                 } else {
16                     return (ty - sy) % tx == 0
17                 }   
18             }
19         }
20         return false
21     }
22 }

---

8ms

 1 class Solution {
 2     func gcd(_ a: Int, _ b: Int) -> Int {
 3         if a < b {
 4             return gcd(b, a)
 5         }
 6         if b == 0 {
 7             return a
 8         }
 9         return gcd(b, a%b)
10     }
11     
12     func reachingPoints(_ sx: Int, _ sy: Int, _ tx: Int, _ ty: Int) -> Bool {
13 
14         var tx = tx
15         var ty = ty
16         while tx >= sx && ty >= sy {
17             if tx == sx && ty == sy {
18                 return true
19             }
20             if tx > ty {
21                 var r = tx%ty
22                 if sx > r {
23                     return ty == sy && (sx-r)%ty == 0
24                 }
25                 tx = r
26             } else {
27                 var r = ty%tx
28                 if sy > r {
29                     return tx == sx && (sy-r)%tx == 0
30                 }
31                 ty = r
32             }
33         }
34         return false
35     }
36 }