Mid/SeniorDynamic Programming
Domino and Tromino Tiling
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 a 2 x n board. Since the answer may be very large, return it 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 1
Input
n = 3Output
5There are five different ways to tile a 2 x 3 board.
Example 2
Input
n = 1Output
1There is only one way to tile a 2 x 1 board.
Constraints
- 1 <= n <= 1000