Package g3601_3700.s3609_minimum_moves_to_reach_target_in_grid

Class Solution

java.lang.Object
g3601_3700.s3609_minimum_moves_to_reach_target_in_grid.Solution
public class Solution extends Object
3609 - Minimum Moves to Reach Target in Grid.

Hard

You are given four integers sx, sy, tx, and ty, representing two points (sx, sy) and (tx, ty) on an infinitely large 2D grid.

You start at (sx, sy).

At any point (x, y), define m = max(x, y). You can either:

  • Move to (x + m, y), or
  • Move to (x, y + m).

Return the minimum number of moves required to reach (tx, ty). If it is impossible to reach the target, return -1.

Example 1:

Input: sx = 1, sy = 2, tx = 5, ty = 4

Output: 2

Explanation:

The optimal path is:

  • Move 1: max(1, 2) = 2. Increase the y-coordinate by 2, moving from (1, 2) to (1, 2 + 2) = (1, 4).
  • Move 2: max(1, 4) = 4. Increase the x-coordinate by 4, moving from (1, 4) to (1 + 4, 4) = (5, 4).

Thus, the minimum number of moves to reach (5, 4) is 2.

Example 2:

Input: sx = 0, sy = 1, tx = 2, ty = 3

Output: 3

Explanation:

The optimal path is:

  • Move 1: max(0, 1) = 1. Increase the x-coordinate by 1, moving from (0, 1) to (0 + 1, 1) = (1, 1).
  • Move 2: max(1, 1) = 1. Increase the x-coordinate by 1, moving from (1, 1) to (1 + 1, 1) = (2, 1).
  • Move 3: max(2, 1) = 2. Increase the y-coordinate by 2, moving from (2, 1) to (2, 1 + 2) = (2, 3).

Thus, the minimum number of moves to reach (2, 3) is 3.

Example 3:

Input: sx = 1, sy = 1, tx = 2, ty = 2

Output: -1

Explanation:

  • It is impossible to reach (2, 2) from (1, 1) using the allowed moves. Thus, the answer is -1.

Constraints:

  • 0 <= sx <= tx <= 109
  • 0 <= sy <= ty <= 109

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minMoves

      public int minMoves(int sx, int sy, int tx, int ty)