LeetCode - Domino and Tromino Tiling

Question Definition

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].

  Java Solution

  public int numTilings(int N) {
    if(N < 2) return 1;
    int kMod = 1000000007;
    long[] dp = new long[N + 1];
    Arrays.fill(dp, 1);
    dp[2] = 2;
    for (int i = 3; i <= N; ++i)
      dp[i] = (dp[i - 3] + dp[i - 1] * 2) % kMod;
    return (int)dp[N];
  }