leetcode-790

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790. Domino and Tromino Tiling

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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].
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class Solution {
public:
    int numTilings(int N) {
        long long MOD = 1e9+7;
        vector<vector<long long>> dp(1005, vector<long long>(4, 0));
        dp[1][0] = 1;
        dp[1][3] = 1;
        
        for(int i=2; 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] + dp[i-1][2] + dp[i-1][3])%MOD; 
        }
        
        return dp[N][3];
    }
};
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