Create snakes-and-ladders.py

Python/snakes-and-ladders.py

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+# Time:  O(n^2)
+# Space: O(n^2)
+
+# On an N x N board, the numbers from 1 to N*N are
+# written boustrophedonically starting from the bottom left of the board,
+# and alternating direction each row.  For example, for a 6 x 6 board,
+# the numbers are written as follows:
+#
+# 36 35 34 33 32 31
+# 25 26 27 28 29 30
+# 24 23 22 21 20 19
+# 13 14 15 16 17 18
+# 12 11 10 09 08 07
+# 01 02 03 04 05 06
+#
+# You start on square 1 of the board (which is always in the last row and first column).
+# Each move, starting from square x, consists of the following:
+#
+# You choose a destination square S with number x+1, x+2, x+3, x+4, x+5, or x+6,
+# provided this number is <= N*N.
+# If S has a snake or ladder, you move to the destination of that snake or ladder.
+# Otherwise, you move to S.
+# 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].
+#
+# 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 continue moving.
+#
+# Return the least number of moves required to reach square N*N.  If it is not possible, return -1.
+#
+# Example 1:
+#
+# Input: [
+# [-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: 
+# At the beginning, you start at square 1 [at row 5, column 0].
+# You decide to move to square 2, and must take the ladder to square 15.
+# You then decide to move to square 17 (row 3, column 5), and must take the snake to square 13.
+# You then decide to move to square 14, and must take the ladder to square 35.
+# You then decide to move to square 36, ending the game.
+# It can be shown that you need at least 4 moves to reach the N*N-th square, so the answer is 4.
+#
+# Note:
+# - 2 <= board.length = board[0].length <= 20
+# - board[i][j] is between 1 and N*N or is equal to -1.
+# - The board square with number 1 has no snake or ladder.
+# - The board square with number N*N has no snake or ladder.
+
+class Solution(object):
+    def snakesAndLadders(self, board):
+        """
+        :type board: List[List[int]]
+        :rtype: int
+        """
+        def coordinate(n, s):
+            a, b = divmod(s-1, n)
+            r = n-1-a
+            c = b if r%2 != n%2 else n-1-b
+            return r, c
+
+        n = len(board)
+        lookup = {1: 0}
+        q = collections.deque([1])
+        while q:
+            s = q.popleft()
+            if s == n*n:
+                return lookup[s]
+            for s2 in xrange(s+1, min(s+6, n*n)+1):
+                r, c = coordinate(n, s2)
+                if board[r][c] != -1:
+                    s2 = board[r][c]
+                if s2 not in lookup:
+                    lookup[s2] = lookup[s]+1
+                    q.append(s2)
+        return -1