Snakes and Ladders — LeetCode 909 Python Solution

The problem

You are given an n x n integer matrix board where the cells are labeled from 1 to n2 in a Boustrophedon style starting from the bottom left of the board (i.e. board[n - 1][0]) and alternating direction each row.

Example

Input

board = [[-1,-1,-1,-1,-1,-1],[-1,-1,-1,-1,-1,-1],[-1,-1,-1,-1,-1,-1],[-1,35,-1,-1,13,-1],[-1,-1,-1,-1,-1,-1],[-1,15,-1,-1,-1,-1]]

Output

4

Explanation

In the beginning, you start at square 1 (at row 5, column 0).

Python solution

class Solution:
    def snakesAndLadders(self, board: List[List[int]]) -> int:
        n = len(board)
        q = deque([1])
        vis = {1}
        ans = 0
        m = n * n
        while q:
            for _ in range(len(q)):
                x = q.popleft()
                if x == m:
                    return ans
                for y in range(x + 1, min(x + 6, m) + 1):
                    i, j = divmod(y - 1, n)
                    if i & 1:
                        j = n - j - 1
                    i = n - i - 1
                    z = y if board[i][j] == -1 else board[i][j]
                    if z not in vis:
                        vis.add(z)
                        q.append(z)
            ans += 1
        return -1

Complexity

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 909. Snakes and Ladders is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

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