How do you solve Minimum White Tiles After Covering With Carpets on LeetCode?

Minimum White Tiles After Covering With Carpets (LeetCode #2209) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * numCarpets) time complexity and O(n * numCarpets) space complexity. Key insight: Using dynamic programming allows us to avoid redundant calculations and efficiently compute results.

What is the time complexity of Minimum White Tiles After Covering With Carpets?

The optimal solution for Minimum White Tiles After Covering With Carpets runs in O(n * numCarpets) time and uses O(n * numCarpets) space. This complexity arises because we are filling a DP table of size n by numCarpets, iterating through each tile and each carpet count.

What is the brute force solution for Minimum White Tiles After Covering With Carpets?

The brute force approach for Minimum White Tiles After Covering With Carpets is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying every possible way to place the carpets on the floor and calculating the number of visible white tiles for each configuration. This method is straightforward but inefficient, especially for larger inputs. The optimal Optimal Solution approach improves this to O(n * numCarpets).

What algorithm or data structure is used to solve Minimum White Tiles After Covering With Carpets?

Minimum White Tiles After Covering With Carpets uses the following concepts: String, Dynamic Programming, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Prefix Sum.

What are the interview tips for Minimum White Tiles After Covering With Carpets?

Always clarify the problem constraints and edge cases before diving into coding. Discuss your thought process and approach with the interviewer to ensure you are on the right track. Practice explaining your code and logic clearly, as communication is key during interviews.

What are common mistakes when solving Minimum White Tiles After Covering With Carpets?

Not considering overlapping carpets, which can lead to incorrect counts of visible tiles. Failing to initialize the DP array correctly, which can cause out-of-bounds errors.

#2209

Minimum White Tiles After Covering With Carpets

Hard

StringDynamic ProgrammingPrefix SumDynamic ProgrammingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n * numCarpets)Space O(n * numCarpets)

The optimal solution uses dynamic programming to efficiently calculate the minimum number of visible white tiles. By breaking the problem down into smaller subproblems, we can build up the solution without redundant calculations.

⚙️

Algorithm

3 steps

1Step 1: Create a DP array where DP[i][j] represents the minimum number of visible white tiles from index i to the end using j carpets.
2Step 2: Iterate through the DP array, filling in values based on previous calculations and the effect of placing carpets.
3Step 3: Use prefix sums to quickly calculate the number of white tiles covered by carpets.

solution.py24 lines

1# Full working Python code
2
3def minWhiteTiles(floor, numCarpets, carpetLen):
4    n = len(floor)
5    dp = [[float('inf')] * (numCarpets + 1) for _ in range(n + 1)]
6    prefixSum = [0] * (n + 1)
7
8    for i in range(n):
9        prefixSum[i + 1] = prefixSum[i] + (1 if floor[i] == '1' else 0)
10
11    for j in range(numCarpets + 1):
12        dp[n][j] = 0
13
14    for i in range(n - 1, -1, -1):
15        for j in range(numCarpets + 1):
16            dp[i][j] = dp[i + 1][j]  # Not using a carpet
17            if j > 0:
18                end = min(i + carpetLen, n)
19                dp[i][j] = min(dp[i][j], prefixSum[end] - prefixSum[i] + dp[end][j - 1])
20
21    return dp[0][numCarpets]
22
23# Example usage
24print(minWhiteTiles('10110101', 2, 2))

ℹ

Complexity note: This complexity arises because we are filling a DP table of size n by numCarpets, iterating through each tile and each carpet count.

1Using dynamic programming allows us to avoid redundant calculations and efficiently compute results.
2Prefix sums help in quickly calculating the number of white tiles in a given range.

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