806. Domino and Tromino Tiling

难度: Medium

题目描述

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 shown above.

Example 2:

Input: n = 1
Output: 1

 

Constraints:

• 1 <= n <= 1000

解题思路

代码实现

解决方案

java

class Solution {
    static final int MOD = 1000000007;

    public int numTilings(int n) {

        if (n == 1) {
            return 1;
        }

        if (n == 2) {
            return 2;
        }
        if (n == 3) {
            return 5;
        }
        int[][] dp = new int[n + 1][4];
        dp[0][3] = 1;
        for (int i = 1; i <= n; i++) {
            dp[i][0] = dp[i - 1][3];
            dp[i][1] = (dp[i - 1][0] + dp[i - 1][2]) % MOD;
            dp[i][2] = (dp[i - 1][0] + dp[i - 1][1]) % MOD;
            dp[i][3] = (((dp[i - 1][0] + dp[i - 1][1]) % MOD + dp[i - 1][2]) % MOD + dp[i - 1][3]) % MOD;
        }

        return dp[n][3];

    }
}