780. Reaching Points

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].

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Solution #1, 因为给定的都是正数，所有可以对比tx跟ty，大的减去小的就是之前的那一对数

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

Solution #2, 跟#1类似，但是我们需要快速收敛。考虑以下例子
2, 12
2, 8
2, 6
2, 4
2, 2

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