73th LeetCode Weekly Contest 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

Note:

N will be in range [1, 1000].

一块区域有--，L（上下两种位置），问2*N有几种放置方式。

首先

x 这种我们叫0

x这种我们叫1

xx这种我们叫2

xxx是怎么得到的呢。一种是x+横着和竖着 xx+竖着 xx+L形（上下两种）

xxx x xx x

于是...dp[i][0]=dp[i-2][0]+dp[i-1][0]+dp[i-1][1]+dp[i-1][2] i表示列数啦

xxxx是怎么得到的呢。xx+L xx+ --

xxx　　　　　　　 xx　 xxx

dp[i][1]=dp[i-2][0]+dp[i-1][2]

xxx同理

xxxx

 class Solution {

 public:

     const int mod = ;

     int dp[][];

     int numTilings(int N) {

         dp[][]=,dp[][]=;

         for(int i=;i<=N;i++){

             dp[i][]=(dp[i-][]%mod+dp[i-][]%mod)%mod+(dp[i-][]%mod+dp[i-][]%mod)%mod;

             dp[i][]=(dp[i-][]%mod+dp[i-][]%mod)%mod;

             dp[i][]=(dp[i-][]%mod+dp[i-][]%mod)%mod;

         }

         return dp[N][]%mod;

     }

 };

巴特西

73th LeetCode Weekly Contest Domino and Tromino Tiling

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