Leetcode #1411: Number of Ways to Paint N × 3 Grid
In this guide, we solve Leetcode #1411 Number of Ways to Paint N × 3 Grid in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: n = 1
Output: 12
Explanation: There are 12 possible way to paint the grid as shown.
Python Solution
class Solution:
def numOfWays(self, n: int) -> int:
mod = 10**9 + 7
f0 = f1 = 6
for _ in range(n - 1):
g0 = (3 * f0 + 2 * f1) % mod
g1 = (2 * f0 + 2 * f1) % mod
f0, f1 = g0, g1
return (f0 + f1) % mod
Complexity
The time complexity is , where is the number of rows in the grid. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.