Number of Ways to Paint N × 3 Grid
Problem Statement
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
Code
Python Code
class Solution:
def numOfWays(self, n: int) -> int:
MOD = 1000000007
P = ['ryr', 'yry', 'gry', 'ryg', 'yrg', 'grg', 'rgr', 'ygr', 'gyr', 'rgy', 'ygy', 'gyg']
nei = [[i for i, x in enumerate(P) if all(a != b for a, b in zip(x, p))] for p in P]
dp = [1] * 12
for i in range(n - 1):
dp = [sum(dp[j] for j in nei[i]) % MOD for i in range(12)]
return sum(dp) % MOD