LeetCode 780. Reaching Points

原题链接在这里：https://leetcode.com/problems/reaching-points/

题目：

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].

题解：

Try reducing tx and ty to sx and sy.

When ty > tx, then the last operation must be tx + val = ty. While(ty > tx) ty - = tx. We could replace by ty %= tx.

Vice versa.

Just check if we could track back to tx = sx, ty = sy + k * sx. Vice versa.

AC Java:

class Solution {
    public boolean reachingPoints(int sx, int sy, int tx, int ty) {
        while(tx > sx && ty > sy){
            if(ty > tx){
                ty %= tx;
            }else{
                tx %= ty;
            }
        }
        
        return sx == tx && sy <= ty && (ty - sy) % sx == 0 ||
            (sy == ty && sx <= tx && (tx - sx) % sy == 0); 
    }
}