LeetCode 790. Domino and Tromino Tiling

原题链接在这里：https://leetcode.com/problems/domino-and-tromino-tiling/

题目：

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].

题解：

Draw some simple examples and find routine.

Let dp[i] denotes ways to tile a 2*i board. 

 

 Use int variable instread of array to save space.

Time Complexity: O(N).

Space: O(1).

AC Java:

class Solution {
    int M = 1000000007;
    public int numTilings(int N) {
        if(N <= 0){
            return 0;
        }
        
        if(N == 1){
            return 1;
        }
        
        if(N == 2){
            return 2;
        }
        
        if(N == 3){
            return 5;
        }
        
        int w1 = 1;
        int w2 = 2;
        int w3 = 5;
        for(int i = 4; i<=N; i++){
            int w4 = (w3*2%M + w1)%M;
            w1 = w2;
            w2 = w3;
            w3 = w4;
        }
        
        return w3;
    }
}

类似Climbing Stairs.