Grid Reachability With Jump/Walk Cells

Problem Overview

You are given a 2D grid of characters representing a board. Each cell is one of:

• 'W' — a walk cell. From here the player moves 1 step to any of the four orthogonal neighbours.
• 'J' — a jump cell. From here the player can jump to any other jump cell in the grid.
• '.' — an obstacle cell. The player cannot move through or land on this cell.

The player starts at the top-left cell (0, 0) of the grid. The goal is to determine if the player can reach the bottom-right cell (n-1, m-1) of the grid.

Constraints

• 1 <= n, m <= 200 (size of the grid)
• grid[i][j] is either 'W', 'J', or '.'.

Examples

1. Example 1:

   • Input: grid = [ ["J", "W", "W", "J"], ["W", "W", "W", "J"], ["W", "J", "W", "W"], ["J", "W", "W", "J"] ]
   • Output: True
   • Explanation: The player can reach the bottom-right cell by jumping from the first jump cell to the last one.

2. Example 2:

   • Input: grid = [ ["J", "W", "W"], ["W", "W", "W"], ["W", "J", "W"] ]
   • Output: False
   • Explanation: There is no way to reach the bottom-right cell.

Solution Approach

1. Identify Jump Cells:

   • Find all the jump cells in the grid and store their coordinates.

2. Breadth-First Search (BFS):

   • Perform BFS from the starting cell (0, 0). During the BFS, consider two types of moves:
     • Moving 1 step to any of the four orthogonal neighbours if the current cell is a walk cell.
     • Jumping to any other jump cell if the current cell is a jump cell.

3. Check Reachability:

   • If the bottom-right cell (n-1, m-1) is reached during the BFS, return True. Otherwise, return False.

Code

`python from collections import deque

def canReach(grid): n, m = len(grid), len(grid[0]) directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] jump_cells = []

# Find all jump cells
for i in range(n):
    for j in range(m):
        if grid[i][j] == 'J':
            jump_cells.append((i, j))

# BFS
queue = deque([(0, 0)])
visited = set((0, 0))

while queue:
    x, y = queue.popleft()
    
    # Check if reached the bottom-right cell
    if x == n - 1 and y == m - 1:
        return True
    
    # Walk cells
    for dx, dy in directions:
        nx, ny = x + dx, y + dy
        if 0 <= nx < n and 0 <= ny < m and grid[nx][ny] != '.' and (nx, ny) not in visited:
            queue.append((nx, ny))
            visited.add((nx, ny))
    
    # Jump cells
    if grid[x][y] == 'J':
        for jx, jy in jump_cells:
            if (jx, jy) not in visited:
                queue.append((jx, jy))
                visited.add((jx, jy))

return False

`

After conducting a thorough search, I found no additional information or variations of this problem on the specified platforms. The problem statement, constraints, examples, and solution approach provided above are based on the excerpt and common problem-solving strategies for grid-based reachability problems. If you have any further details or specific requirements, feel free to ask.