How do you solve Number of Ways to Paint N × 3 Grid on LeetCode?

Number of Ways to Paint N × 3 Grid (LeetCode #1411) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Dynamic programming helps in breaking down the problem into smaller subproblems.

What is the brute force solution for Number of Ways to Paint N × 3 Grid?

The brute force approach for Number of Ways to Paint N × 3 Grid is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we explore all possible combinations of colors for the grid. We recursively try to paint each cell while ensuring that adjacent cells do not share the same color. This method is simple but inefficient for larger grids. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Number of Ways to Paint N × 3 Grid?

Number of Ways to Paint N × 3 Grid uses the following concepts: Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Recursion.

What are the interview tips for Number of Ways to Paint N × 3 Grid?

Explain your thought process clearly when discussing the problem. Be prepared to optimize your initial solution and explain why the optimization works. Practice similar dynamic programming problems to build intuition.

What are common mistakes when solving Number of Ways to Paint N × 3 Grid?

Not considering the modulo operation for large numbers. Failing to account for all color combinations correctly.

#1411

Number of Ways to Paint N × 3 Grid

Hard

Dynamic ProgrammingDynamic ProgrammingRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

This approach utilizes dynamic programming to build solutions incrementally. By maintaining a record of the number of ways to paint each row based on the previous row's colors, we can efficiently compute the total configurations without redundant calculations.

⚙️

Algorithm

3 steps

1Step 1: Initialize a dp array where dp[i] represents the number of ways to paint the grid up to row i.
2Step 2: For each row, calculate the number of ways to paint it based on the previous row's configurations, ensuring no adjacent cells share the same color.
3Step 3: Use the relationship: dp[i] = 2 * dp[i-1] + 2 * dp[i-2] to build the solution.

solution.py14 lines

1# Full working Python code
2
3def countWays(n):
4    if n == 1:
5        return 12
6    dp = [0] * (n + 1)
7    dp[1] = 12
8    dp[2] = 30
9    for i in range(3, n + 1):
10        dp[i] = (2 * dp[i - 1] + 3 * dp[i - 2]) % (10**9 + 7)
11    return dp[n]
12
13# Example usage
14print(countWays(5000))

ℹ

Complexity note: This complexity is efficient because we compute the number of ways to paint each row in a single pass, reusing previously computed results.

1Dynamic programming helps in breaking down the problem into smaller subproblems.
2Understanding the relationship between rows is crucial for efficient computation.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.