Problem Statement

You are given an m x n binary matrix grid where each cell is either empty (0) or has an obstacle (1). You can move up, down, left, or right, but only through empty cells. You can remove up to k obstacles along the way.

Return the shortest path from the top-left corner (0, 0) to the bottom-right corner (m - 1, n - 1). If it's not possible to reach the end, return -1.

Examples

Example 1

• Input: k = 1, grid =

[[0, 1, 0, 0],
 [1, 1, 0, 1],
 [0, 0, 0, 0],
 [0, 1, 1, 0]]

• Expected Output: 6

• Justification: You can remove one obstacle to create a path from (0, 0) to (3, 3). The path can be (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (2,3) → (3,3). Here, we have removed the obstacle from (0, 1) position.

Example 2

• Input: k = 2, grid =

  [[0, 0, 0],
   [1, 1, 0],
   [1, 1, 0],
   [0, 0, 0]]

• Expected Output: 5
• Justification: You can remove two obstacles to create a path from (0, 0) to (3, 2). The path can be (0,0) → (0,1) → (0,2) → (1,2) → (2,2) -> (3, 2). Here, we don't need to remove any obstacles.

Example 3

• Input: k = 3, grid =

 [[0, 0, 1],
  [0, 1, 0],
  [1, 0, 0],
  [0, 1, 0]]
 

• Expected Output: 5

• Justification: You can remove three obstacles to create a path from (0, 0) to (3, 2). The path can be (0,0) → (0,1) → (0,2) → (1,2) → (2,2) → (3,2). Here, we have removed the obstacle from (0, 2) position.

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 40
• 1 <= k <= m * n
• grid[i][j] is either 0 or 1.
• grid[0][0] == grid[m - 1][n - 1] == 0

Try it yourself

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