909. Snakes and Ladders

BFS, Array, Matrix · 17 May 2024

Problem Statement

link: LeetCode.cn LeetCode 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.

You start on square 1 of the board. In each move, starting from square curr, do the following:

Choose a destination square next with a label in the range [curr + 1, min(curr + 6, n2)]. This choice simulates the result of a standard 6-sided die roll: i.e., there are always at most 6 destinations, regardless of the size of the board. If next has a snake or ladder, you must move to the destination of that snake or ladder. Otherwise, you move to next. The game ends when you reach the square n2. A board square on row r and column c has a snake or ladder if board[r][c] != -1. The destination of that snake or ladder is board[r][c]. Squares 1 and n2 do not have a snake or ladder.

Note that you only take a snake or ladder at most once per move. If the destination to a snake or ladder is the start of another snake or ladder, you do not follow the subsequent snake or ladder.

For example, suppose the board is [[-1,4],[-1,3]], and on the first move, your destination square is 2. You follow the ladder to square 3, but do not follow the subsequent ladder to 4. Return the least number of moves required to reach the square n2. If it is not possible to reach the square, return -1.

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

Input: board = [[-1,-1],[-1,3]] Output: 1

Solution Approach

Use Breadth-First Search (BFS) to explore all possible moves from each square, updating the position based on snakes and ladders, and track the minimum number of moves to reach the final square.

Algorithm

Breadth-First Search (BFS): Use BFS to explore all possible moves from each square, ensuring the shortest path to the final square is found.
Position Calculation: Convert the 1D square number to 2D board coordinates, considering the alternating direction of rows.
Snake and Ladder Adjustment: Update the position based on the presence of snakes and ladders and track visited squares to avoid redundant processing.

Implement

    class Solution:
    def snakesAndLadders(self, board: List[List[int]]) -> int:
        # // q = [(number, step)] 
        # // loop 6 possible step
        # //      move index
        # //      get real r & c
        # //      check if (r, c) > 0 move index
        # //      check if reach the end & return
        # //      if not visited: add to visited and q
        # //cannot reach return -1
        n = len(board)
        target = n * n
        queue = [(1, 0)]
        visited = [[False] * n for _ in range(n)]
        while queue:
            curr, cnt = queue.pop(0)
            cnt += 1
            for i in range(curr + 1, min(curr + 6, target) + 1):
                r, c = n - 1 - (i - 1) // n, (i - 1) % n
                c += (n - 1 - 2 * c) * ((n - 1 - r) & 1)
                if visited[r][c]: continue
                visited[r][c] = True
                next_ = i if board[r][c] == k-1 else board[r][c]
                if next_ == target: return cnt
                queue.append((next_, cnt))
        return -1