790. Domino and Tromino Tiling

We have two types of tiles: a 2x1 domino shape, and an "L" tromino shape. These shapes may be rotated.

```XX  <- domino

XX  <- "L" tromino
X
```

Given N, how many ways are there to tile a 2 x N board? Return your answer 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:
Input: 3
Output: 5
Explanation:
The five different ways are listed below, different letters indicates different tiles:
XYZ XXZ XYY XXY XYY
XYZ YYZ XZZ XYY XXY```

Note:

• N  will be in range `[1, 1000]`.

790. Domino and Tromino Tiling
``````struct Solution;

const MOD: usize = 1_000_000_007;

impl Solution {
fn num_tilings(n: i32) -> i32 {
let n = n as usize;
if n == 0 {
return 0;
}
let mut memo: Vec<usize> = vec![0; n + 1];
Self::dp(n, &mut memo) as i32
}
fn dp(n: usize, memo: &mut Vec<usize>) -> usize {
match n {
0 => 1,
1 => 1,
2 => 2,
3 => 5,
_ => {
if memo[n] > 0 {
return memo[n];
}
let mut res = 0;
res += Self::dp(n - 3, memo);
res %= MOD;
res += 2 * Self::dp(n - 1, memo);
res %= MOD;
memo[n] = res;
res
}
}
}
}

#[test]
fn test() {
let n = 3;
let res = 5;
assert_eq!(Solution::num_tilings(n), res);
let n = 4;
let res = 11;
assert_eq!(Solution::num_tilings(n), res);
}
``````