#1210

Hard

auto_awesomeArray plus Breadth-First Search

LeetCode Problem Workspace

Minimum Moves to Reach Target with Rotations

Find the minimum moves for a 2-cell snake to reach the bottom-right corner using rotations and BFS traversal in a grid.

Problem Statement

You are given an n*n grid with empty cells (0) and blocked cells (1). A snake spans two adjacent cells and starts at the top-left corner occupying positions (0,0) and (0,1). The goal is to move the snake to the bottom-right corner occupying positions (n-1,n-2) and (n-1,n-1). The snake can move right, move down, or rotate clockwise/counterclockwise if the space is clear.

Return the minimum number of moves required for the snake to reach the target, or -1 if it cannot reach the destination. Each move must account for both the snake's head and tail positions and its current orientation, ensuring it does not pass through blocked cells.

Examples

Example 1

Input: grid = [[0,0,0,0,0,1], [1,1,0,0,1,0], [0,0,0,0,1,1], [0,0,1,0,1,0], [0,1,1,0,0,0], [0,1,1,0,0,0]]

Output: 11

One possible solution is [right, right, rotate clockwise, right, down, down, down, down, rotate counterclockwise, right, down].

Example 2

Input: grid = [[0,0,1,1,1,1], [0,0,0,0,1,1], [1,1,0,0,0,1], [1,1,1,0,0,1], [1,1,1,0,0,1], [1,1,1,0,0,0]]

Output: 9

Example details omitted.

Constraints

2 <= n <= 100
0 <= grid[i][j] <= 1
It is guaranteed that the snake starts at empty cells.

Solution Approach

Use Breadth-First Search

Model each state as the snake's head position, tail position, and orientation. Use a queue to perform BFS, exploring all valid moves from each state while tracking visited configurations to prevent redundant processing.

Check Valid Moves and Rotations

For each state, attempt to move right, move down, or rotate. Ensure all involved cells are empty before performing the move or rotation. Consider both horizontal and vertical orientations when applying rotations.

Track Moves Efficiently

Maintain a visited set to store tuples of (head, tail, orientation) to avoid revisiting states. Increment move count with each BFS layer to ensure the first time the target is reached corresponds to the minimum number of moves.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n^2 * 2) considering all positions and orientations. Space complexity is also O(n^2 * 2) for visited states and BFS queue storage.

What Interviewers Usually Probe

Candidate must correctly track snake orientation and positions separately.
Look for BFS usage to ensure minimal moves are found instead of DFS.
Check that rotations only occur when the required 2x2 space is empty.

Common Pitfalls or Variants

Common pitfalls

Failing to account for orientation when checking valid moves.
Forgetting to mark states as visited leading to cycles in BFS.
Attempting rotations without verifying all necessary cells are empty.

Follow-up variants

Snake length can be extended to more than 2 cells with similar BFS logic.
Allow diagonal moves and rotations for more complex maneuvering.
Introduce weighted moves where certain directions cost more, adjusting BFS to Dijkstra.

FAQ

What pattern does this problem follow?

It follows the Array plus Breadth-First Search pattern, tracking positions and orientations to compute minimal moves.

How do I handle rotations in the BFS?

Only perform rotations when the 2x2 area around the snake is empty, updating orientation and adding the new state to the queue.

What should I return if the snake cannot reach the target?

Return -1 if BFS completes without reaching the bottom-right target configuration.

What data structure is best for tracking visited states?

Use a set storing tuples of (head position, tail position, orientation) to efficiently avoid revisiting states.

Can GhostInterview show the exact moves sequence for Minimum Moves to Reach Target with Rotations?

Yes, it can generate the step-by-step move sequence, showing right, down, and rotation moves to reach the target efficiently.

terminal

Solution

Solution 1: BFS

The problem asks for the minimum number of moves for the snake to reach the target position from the starting position. We consider using Breadth-First Search (BFS) to solve it.

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class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:
        def move(i1, j1, i2, j2):
            if 0 <= i1 < n and 0 <= j1 < n and 0 <= i2 < n and 0 <= j2 < n:
                a, b = i1 * n + j1, i2 * n + j2
                status = 0 if i1 == i2 else 1
                if (a, status) not in vis and grid[i1][j1] == 0 and grid[i2][j2] == 0:
                    q.append((a, b))
                    vis.add((a, status))

        n = len(grid)
        target = (n * n - 2, n * n - 1)
        q = deque([(0, 1)])
        vis = {(0, 0)}
        ans = 0
        while q:
            for _ in range(len(q)):
                a, b = q.popleft()
                if (a, b) == target:
                    return ans
                i1, j1 = a // n, a % n
                i2, j2 = b // n, b % n
                # 尝试向右平移（保持身体水平/垂直状态）
                move(i1, j1 + 1, i2, j2 + 1)
                # 尝试向下平移（保持身体水平/垂直状态）
                move(i1 + 1, j1, i2 + 1, j2)
                # 当前处于水平状态，且 grid[i1 + 1][j2] 无障碍，尝试顺时针旋转90°
                if i1 == i2 and i1 + 1 < n and grid[i1 + 1][j2] == 0:
                    move(i1, j1, i1 + 1, j1)
                # 当前处于垂直状态，且 grid[i2][j1 + 1] 无障碍，尝试逆时针旋转90°
                if j1 == j2 and j1 + 1 < n and grid[i2][j1 + 1] == 0:
                    move(i1, j1, i1, j1 + 1)
            ans += 1
        return -1

Continue Practicing

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