Leetcode: Domino and Tromino Tiling

Domino and Tromino Tiling



Similar Problems:


We have two types of tiles: a 2×1 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].

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.


## Blog link: https://code.dennyzhang.com/domino-and-tromino-tiling
## Basic Ideas: dynamic programming
##
## Complexity: Time O(n), Space O(1)
class Solution:
    def numTilings(self, N):
        """
        :type N: int
        :rtype: int
        """
        if N==1: return 1
        if N==2: return 2
        if N==3: return 5
        mod_num = pow(10, 9)+7
        v3,v2,v1 = 5,2,1
        sum_v=4

        for i in range(4, N+1):
            v = (v3+v2+sum_v) % mod_num
            v3,v2,v1 = v,v3,v2
            sum_v=sum_v+v1*2
        return v3

# s = Solution()
# print(s.numTilings(4)) # 11
# print(s.numTilings(5)) # 24
# print(s.numTilings(6)) # 53
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