Problem
You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes.
Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it 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 1:
Input: n = 3
Output: 5
Explanation: The five different ways are show above.
Example 2:
Input: n = 1
Output: 1
Constraints:
1 <= n <= 1000
Solution (Java)
class Solution {
public int numTilings(int n) {
if (n == 1) {
return 1;
} else if (n == 2) {
return 2;
} else if (n == 3) {
return 5;
} else if (n == 4) {
return 11;
} else if (n == 5) {
return 24;
}
long[] dp = new long[n + 1];
dp[0] = 0;
dp[1] = 1;
dp[2] = 2;
dp[3] = 5;
dp[4] = 11;
dp[5] = 24;
dp[6] = 53;
for (int i = 7; i <= n; i++) {
dp[i] = ((dp[i - 1] * 2) + dp[i - 3]) % 1000000007;
}
return (int) dp[n] % 1000000007;
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).