LeetCode-in-Java

2543. Check if Point Is Reachable

Hard

There exists an infinitely large grid. You are currently at point (1, 1), and you need to reach the point (targetX, targetY) using a finite number of steps.

In one step, you can move from point (x, y) to any one of the following points:

Given two integers targetX and targetY representing the X-coordinate and Y-coordinate of your final position, return true if you can reach the point from (1, 1) using some number of steps, and false otherwise.

Example 1:

Input: targetX = 6, targetY = 9

Output: false

Explanation: It is impossible to reach (6,9) from (1,1) using any sequence of moves, so false is returned.

Example 2:

Input: targetX = 4, targetY = 7

Output: true

Explanation: You can follow the path (1,1) -> (1,2) -> (1,4) -> (1,8) -> (1,7) -> (2,7) -> (4,7).

Constraints:

Solution

public class Solution {
    public boolean isReachable(int x, int y) {
        int g = gcd(x, y);
        return (g & (g - 1)) == 0;
    }

    private int gcd(int x, int y) {
        while (x != 0) {
            int tmp = x;
            x = y % x;
            y = tmp;
        }
        return y;
    }
}