README_EN.md

2543. Check if Point Is Reachable

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Description

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:

• (x, y - x)
• (x - y, y)
• (2 * x, y)
• (x, 2 * y)

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:

• 1 <= targetX, targetY <= 109

Solutions

Python3

class Solution:
    def isReachable(self, targetX: int, targetY: int) -> bool:
        x = gcd(targetX, targetY)
        return x & (x - 1) == 0

Java

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

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}

C++

class Solution {
public:
    bool isReachable(int targetX, int targetY) {
        int x = gcd(targetX, targetY);
        return (x & (x - 1)) == 0;
    }
};

Go

func isReachable(targetX int, targetY int) bool {
	x := gcd(targetX, targetY)
	return x&(x-1) == 0
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

TypeScript

function isReachable(targetX: number, targetY: number): boolean {
    const x = gcd(targetX, targetY);
    return (x & (x - 1)) === 0;
}

function gcd(a: number, b: number): number {
    return b == 0 ? a : gcd(b, a % b);
}

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