790. Domino and Tromino Tiling
Đề Bài
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
Thuật Toán & Kỹ Thuật
⏱️ Thời gian
O(n²)
💾 Không gian
O(n)
Lời Giải
Python
0790-domino-and-tromino-tiling.py
class Solution:
def numTilings(self, n: int) -> int:
dp = [0 for i in range(1001)]
dp[1] = 1
dp[2] = 2
dp[3] = 5
for i in range(4, n + 1):
dp[i] = (2 * dp[i - 1] + dp[i - 3]) % (10 ** 9 + 7)
return dp[n]