# 790. Domino and Tromino Tiling 多米诺和托米诺平铺

## # 题目描述：

We have two types of tiles: a 2x1 domino shape, and an "L" tromino shape. These shapes may be rotated.

XX  <- domino

XX  <- "L" tromino
X

Given N, how many ways are there to tile a 2 x N board? Return your answer modulo 10^9 + 7.

(In a tiling, every square must be covered by a tile. Two tilings are different if and only if there are two 4-directionally adjacent cells on the board such that exactly one of the tilings has both squares occupied by a tile.)

Example:

Input: 3
Output: 5
Explanation:
The five different ways are listed below, different letters indicates different tiles:
XYZ XXZ XYY XXY XYY
XYZ YYZ XZZ XYY XXY

Note:

1. N will be in range [1, 1000].

## # 解题方法

class Solution:
def numTilings(self, N):
"""
:type N: int
:rtype: int
"""
dp = [[0] * 2 for _ in range(N + 1)]
dp[0][0] = 1
dp[1][0] = 1
for i in range(2, N + 1):
dp[i][0] = (dp[i - 1][0] + dp[i - 2][0] + 2 * dp[i - 1][1]) % (10 ** 9 + 7)
dp[i][1] = (dp[i - 2][0] + dp[i - 1][1]) % (10 ** 9 + 7)
return dp[-1][0]