Solution Explanation: Minimum Moves to Reach Target with Rotations

This problem involves finding the minimum number of moves a snake-like shape (occupying two adjacent cells) needs to reach the bottom-right corner of a grid, given obstacles. The snake can move right, down, or rotate clockwise/counterclockwise under certain conditions. Breadth-First Search (BFS) is an ideal approach to solve this.

Approach: Breadth-First Search (BFS)

BFS systematically explores the grid, ensuring that the shortest path is found first. Here's how it's applied:

1. State Representation: The snake's state is defined by the coordinates of its head and tail. Crucially, we also need to track the snake's orientation (horizontal or vertical). This is because the rotation moves are dependent on the orientation.

2. Queue: A queue (q) stores the snake's states (head and tail coordinates and orientation) to be explored. We start with the initial state of the snake.

3. Visited Set: A set (vis) keeps track of visited states to avoid cycles and redundant exploration. It's essential to check if a state has been visited before adding it to the queue. The set uses a tuple or equivalent structure to store the state information (head coordinate, orientation).

4. Iteration: The BFS algorithm iteratively dequeues a state, checks if it's the target, and if not, explores all possible next states. Each time we explore a new state, we check if that state can be reached and whether it has already been visited.

5. Move Generation: For each state, we generate possible next states based on the four allowed moves (right, down, clockwise rotation, counterclockwise rotation). These moves are only valid if they don't involve moving into a blocked cell.

6. Target Check: If a state is the target, we return the number of moves (distance) from the start.

7. No Path: If the queue becomes empty without finding the target, it means no path exists, so we return -1.

Time and Space Complexity

• Time Complexity: O(N^2), where N is the size of the grid. In the worst case, BFS might visit all possible snake configurations within the grid.
• Space Complexity: O(N^2) due to the queue and the visited set. Both can store up to all possible configurations of the snake.

Code Implementation (Python)

from collections import deque
 
def minimumMoves(grid):
    n = len(grid)
    target = (n * n - 2, n * n - 1)
    q = deque([(0, 1, 0)]) # (head_index, tail_index, orientation: 0-horizontal, 1-vertical)
    vis = {(0, 0)} # Set to store visited states
 
    ans = 0
    while q:
        for _ in range(len(q)):
            head, tail, orientation = q.popleft()
            if (head, tail) == target:
                return ans
 
            # Generate next states (right, down, rotate)
            # ... (Code to generate and check valid next states using move function) ...
 
        ans += 1
    return -1
 
def move(grid, head, tail, orientation, q, vis, n):
    # This function handles generating the next possible states and checking
    # their validity before adding to the queue.  The details depend on the specific
    # orientation and available moves (right, down, rotate).
    #  ... (Implementation details for generating and checking valid next states) ...

Note: The move function in the Python code is not fully implemented. It would contain the logic for checking the validity of each move (right, down, clockwise, counterclockwise rotation) given the snake's current head, tail, and orientation, as well as the grid's obstacles. The other language examples in the original response provide a complete implementation of this logic. The core BFS structure remains the same across all languages.