Domino and Tromino Tiling — LeetCode 790 Python Solution

The problem

You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes.

Example

Input

n = 3

Output

5

Explanation

The five different ways are shown above.

Python solution

class Solution:
    def numTilings(self, n: int) -> int:
        f = [1, 0, 0, 0]
        mod = 10**9 + 7
        for i in range(1, n + 1):
            g = [0] * 4
            g[0] = (f[0] + f[1] + f[2] + f[3]) % mod
            g[1] = (f[2] + f[3]) % mod
            g[2] = (f[1] + f[3]) % mod
            g[3] = f[0]
            f = g
        return f[0]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 790. Domino and Tromino Tiling is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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