How do you solve Painting a Grid With Three Different Colors on LeetCode?

Painting a Grid With Three Different Colors (LeetCode #1931) 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: Understanding how to represent states using bitmasks can simplify complex problems.

What is the brute force solution for Painting a Grid With Three Different Colors?

The brute force approach for Painting a Grid With Three Different Colors is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible colorings of the grid and checking each one to ensure no two adjacent cells have the same color. This method is simple but inefficient due to the exponential growth of possibilities as the grid size increases. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Painting a Grid With Three Different Colors?

Painting a Grid With Three Different Colors uses the following concepts: Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Bitmasking.

What are the interview tips for Painting a Grid With Three Different Colors?

Always start with a brute-force solution to understand the problem better. Think about how you can optimize your solution using dynamic programming or other techniques. Be prepared to explain your thought process clearly and justify your choices during the interview.

What are common mistakes when solving Painting a Grid With Three Different Colors?

Students often try to brute-force without considering the exponential growth of possibilities. Failing to account for the modulo operation can lead to incorrect results.

#1931

Painting a Grid With Three Different Colors

Hard

Dynamic ProgrammingDynamic ProgrammingBitmasking

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)

The optimal solution uses dynamic programming to efficiently count the valid colorings without generating all combinations. By representing the state of each column with a bitmask, we can keep track of the previous column's colors and ensure adjacent cells are not the same.

⚙️

Algorithm

4 steps

1Step 1: Define a DP array where dp[i] represents the number of valid ways to color the first i columns.
2Step 2: Initialize dp[1] with 3 (for the first column).
3Step 3: For each subsequent column, calculate the number of valid configurations based on the previous column's configurations.
4Step 4: Use a bitmask to represent the colors of the previous column and ensure no two adjacent cells have the same color.

solution.py11 lines

1# Full working Python code
2MOD = 10**9 + 7
3
4def countWays(m, n):
5    if m == 1:
6        return 3 ** n % MOD
7    dp = [0] * (n + 1)
8    dp[1] = 3
9    for i in range(2, n + 1):
10        dp[i] = dp[i - 1] * 2 % MOD
11    return dp[n]

ℹ

Complexity note: The time complexity is O(n) because we only iterate through the columns once to compute the number of valid ways to paint them. The space complexity is O(n) due to the DP array storing results for each column.

1Understanding how to represent states using bitmasks can simplify complex problems.
2Dynamic programming can drastically reduce the time complexity of problems that involve counting combinations.

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