790. 多米诺和托米诺平铺
790. 多米诺和托米诺平铺
题目
You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes.
Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it modulo 109 + 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 1:
Input: n = 3
Output: 5
Explanation: The five different ways are show above.
Example 2:
Input: n = 1
Output: 1
Constraints:
1 <= n <= 1000
题目大意
有两种形状的瓷砖：一种是 2 x 1 的多米诺形，另一种是形如 "L" 的托米诺形。两种形状都可以旋转。
给定整数 n ，返回可以平铺 2 x n 的面板的方法的数量。返回对 109 + 7 取模 的值。
平铺指的是每个正方形都必须有瓷砖覆盖。两个平铺不同，当且仅当面板上有四个方向上的相邻单元中的两个，使得恰好有一个平铺有一个瓷砖占据两个正方形。
示例 1:
输入: n = 3
输出: 5
解释: 五种不同的方法如上所示。
示例 2:
输入: n = 1
输出: 1
提示：
1 <= n <= 1000
解题思路
复杂度分析
- 时间复杂度：
O()， - 空间复杂度：
O()，
代码