<p>You have two types of tiles: a <code>2 x 1</code> domino shape and a tromino shape. You may rotate these shapes.</p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/15/lc-domino.jpg" style="width: 362px; height: 195px;" />
<p>Given an integer n, return <em>the number of ways to tile an</em> <code>2 x n</code> <em>board</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>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.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/15/lc-domino1.jpg" style="width: 500px; height: 226px;" />
<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> The five different ways are show above.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

class Solution 
{
private:
    int ways(int i, int j, vector<vector<long long>>&dp)
    {
        int MOD = 1000000007;
        if(i<=0)
        {
            return 0;
        }
        if(i==1)
        {
            return 1;
        }
        if(i==2)
        {
            return 2;
        }
        if(dp[i][j]!=-1)
        {
            return dp[i][j];
        }
        long long result=0;
        if(j==0)
        {
            result = ((long long)ways(i-1, 0, dp) + (long long)ways(i-2, 0, dp)  + (long long)ways(i-2, 1, dp) + (long long)ways(i-2, 2, dp))%MOD;   
        }
        else if(j==1)
        {
            result  = ((long long)ways(i-1, 0, dp) + (long long)ways(i-1, 2, dp))%MOD;
        }
        else
        {
            result = ((long long)ways(i-1, 0, dp) + (long long)ways(i-1, 1, dp))%MOD;
        }
        return dp[i][j] = result;
    }
public:
    int numTilings(int n) 
    {
        int MOD =1000000007;
        vector<vector<long long>>dp(n+1, vector<long long>(3, -1));
        return ways(n, 0, dp)%MOD;
    }
};
9200