2543. Check if Point Is Reachable
Hard44.8% acceptance10,730 / 23,940 submissions
Asked by 1 company
Topics
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
Hints
Hint 1
Let’s go in reverse order, from (targetX, targetY) to (1, 1). So, now we can move from (x, y) to (x+y, y), (x, y+x), (x/2, y) if x is even, and (x, y/2) if y is even.
Hint 2
When is it optimal to use the third and fourth operations?
Hint 3
Think how GCD of (x, y) is affected if we apply the first two operations.
Hint 4
How can we check if we can reach (1, 1) using the GCD value calculate above?