Snakes and Ladders

You are given an n x n integer matrix board where the cells are labeled from 1 to n^2 in a Boustrophedon style starting from the bottom left of the board, at 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, n^2)].
  • This choice simulates the result of a standard 6-sided die roll, so 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 square n^2.

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 n^2 are not the starting points of any snake or ladder.

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

Return the least number of dice rolls required to reach square n^2. If it is not possible to reach the square, return -1.

Example 1
-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
Inputboard = [[-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]]
Output4
The lowest possible sequence takes four dice rolls: move to square 2 and ladder to 15, move to square 17 and snake to 13, move to square 14 and ladder to 35, then move to square 36.
Example 2
-1 -1
-1  3
Inputboard = [[-1,-1],[-1,3]]
Output1
From square 1, one dice roll can choose square 2, then the ladder moves directly to square 3, which is the final square.

Constraints

  • n == board.length == board[i].length
  • 2 <= n <= 20
  • board[i][j] is either -1 or in the range [1, n^2].
  • The squares labeled 1 and n^2 are not the starting points of any snake or ladder.

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