leetcode 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

思路：分3个状态，第i列上边凸出，下边凸出，和平的。如图，那么状态转换如图中公式。

转载注明出处http://www.cnblogs.com/pk28/p/8470177.html

class Solution {
public:
    const int mod = 1000000007;
    int dp[1100][3];
    int numTilings(int N) {
        dp[0][0] = dp[1][0] = 1;
        for (int i = 2; i <= N; ++i) {
            dp[i][0] = ((dp[i-1][0] + dp[i-2][0])%mod + (dp[i-1][1] + dp[i-1][2])%mod)%mod;
            dp[i][1] = (dp[i-2][0] + dp[i-1][2])%mod;
            dp[i][2] = (dp[i-2][0] + dp[i-1][1])%mod;
        }
        return dp[N][0];
    }
};