Row Bombing Codechef Solution

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Row Bombing Codechef Solution

Row Bombing Codechef Solution

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Problem

There is an N \times M grid, with rows numbered 1 to N from top to bottom, and columns 1 to M from left to right.

Chef starts at cell (1, 1) and wants to reach cell (N, M). However, some cells contain walls. Chef can move from their current cell to any adjacent cell (a cell which shares an edge) within the grid that does not contain a wall. So it may be possible initially that all of Chef’s paths to (N, M) are blocked by walls.

To get around this, Chef can call an airstrike on any row and annihilate all walls present in that row. More formally, if Chef chooses row i (1 \leq i \leq N), then any walls in cells (i, 1), (i, 2) \ldots (i, M) are destroyed. Once a wall is destroyed, the cell becomes freely passable.

Since airstrikes are expensive, help Chef find the minimum number of airstrikes Chef must call to guarantee that Chef can reach (N, M) from (1, 1).

Input Format

  • The first line contains a single integer T — the number of test cases. Then the test cases follow.
  • The first line of each test case contains two integers N and M — the number of rows and the number of columns in the grid.
  • The next N lines contain M characters each, describing the grid. The character at the i-th row and j-th column S_{i, j} is \texttt{‘.’} if the cell (i, j) is empty and \texttt{‘\#’} if there is a wall.

Output Format

For each test case, output on a new line the minimum number of airstrikes Chef must call to guarantee that Chef can reach (N, M) from (1, 1).

Constraints

  • 1 \leq T \leq 2 \cdot 10^5
  • 2 \leq N \times M \leq 5 \cdot 10^5
  • S_{i, j} \in \{\texttt{‘.’}, \texttt{‘\#’}\}
  • The sum of N \times M over all test cases does not exceed 5 \cdot 10^5.
  • It is guaranteed that the starting cell (1, 1) is not blocked by a wall.

Sample 1:

Input

Output

5
1 2
..
1 4
.##.
4 1
.
#
#
.
3 2
.#
##
##
3 3
.##
#.#
##.
0
1
2
2
1

Explanation:

Test case 1:
Chef does not need to call any airstrikes. Chef can follow the path (1, 1) \rightarrow (1, 2).

Test case 2:
Chef must call an airstrike on row 1. This will destroy the walls at (1, 2) and (1, 3). Chef can then follow the path (1, 1) \rightarrow (1, 2) \rightarrow (1, 3) \rightarrow (1, 4).

Test case 3:
Chef must call airstrikes on rows 2 and 3. This will destroy the walls at (2, 1) and (3, 1) respectively. Chef can then follow the path (1, 1) \rightarrow (2, 1) \rightarrow (3, 1) \rightarrow (4, 1).

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SOLUTION

Row Bombing Codechef Solution

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