1411. Number of Ways to Paint N × 3 Grid

Problem Link

Description

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You have a grid of size n x 3 and you want to paint each cell of the grid with exactly one of the three colors: Red, Yellow, or Green while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).

Given n the number of rows of the grid, return the number of ways you can paint this grid. As the answer may grow large, the answer must be computed modulo 109 + 7.

 

Example 1:

Input: n = 1
Output: 12
Explanation: There are 12 possible way to paint the grid as shown.

Example 2:

Input: n = 5000
Output: 30228214

 

Constraints:

• n == grid.length
• 1 <= n <= 5000

Solution

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Python3

class Solution:
    def numOfWays(self, n: int) -> int:
        a121, a123, mod = 6, 6, 10**9 + 7
        for i in range(n - 1):
            a121, a123 = a121 * 3 + a123 * 2, a121 * 2 + a123 * 2
        return (a121 + a123) % mod