Is Minimum White Tiles After Covering With Carpets easy or hard?

Minimum White Tiles After Covering With Carpets is classified as a Hard problem. The difficulty comes from modeling overlapping carpet placements and choosing the optimal placement strategy using dynamic programming.

Minimum White Tiles After Covering With Carpets Python/Java solution

Most implementations use a DP table or memoized recursion. Python solutions typically use recursion with caching or a 2D DP list, while Java implementations often use iterative DP arrays. Both achieve O(n * k) time complexity.

How to solve Minimum White Tiles After Covering With Carpets in O(n)?

Pure O(n) is generally not achievable because the number of carpets introduces another dimension of decisions. However, prefix sums allow constant-time range queries, and the dynamic programming transitions still run in O(n * k). This is considered optimal for the problem constraints.

What is the best approach for Minimum White Tiles After Covering With Carpets?

Dynamic Programming is the most reliable approach. It tracks the minimum uncovered white tiles for each position and number of carpets used. By deciding whether to place a carpet or leave a tile uncovered, the DP guarantees the optimal arrangement with O(n * k) time complexity.

Is Minimum White Tiles After Covering With Carpets asked at Google/Amazon/Meta?

Problems involving interval coverage, dynamic programming decisions, and prefix sums frequently appear in interviews at companies like Google, Amazon, and Meta. This problem reflects the same pattern of optimizing coverage over a sequence with limited resources.

What data structure is used in Minimum White Tiles After Covering With Carpets?

The main technique uses dynamic programming arrays to track states and prefix sum arrays to compute the number of white tiles in any interval quickly. The input itself is processed as a string representing the floor.

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

The optimal dynamic programming solution runs in O(n * k) time where n is the floor length and k is the number of carpets. Each state represents a prefix of the floor and the number of carpets used. Space complexity is also O(n * k) unless optimized.

Description Hints 3 Solution Video 17:07

2209. Minimum White Tiles After Covering With Carpets

Hard39.3% acceptance1 company

You are given a 0-indexed binary string floor, which represents the colors of tiles on a floor:

floor[i] = '0' denotes that the i^th tile of the floor is colored black.
On the other hand, floor[i] = '1' denotes that the i^th tile of the floor is colored white.

You are also given numCarpets and carpetLen. You have numCarpets black carpets, each of length carpetLen tiles. Cover the tiles with the given carpets such that the number of white tiles still visible is minimum. Carpets may overlap one another.

Return the minimum number of white tiles still visible.

Example 1:

Input: floor = "10110101", numCarpets = 2, carpetLen = 2
Output: 2
Explanation: 
The figure above shows one way of covering the tiles with the carpets such that only 2 white tiles are visible.
No other way of covering the tiles with the carpets can leave less than 2 white tiles visible.

Example 2:

Input: floor = "11111", numCarpets = 2, carpetLen = 3
Output: 0
Explanation: 
The figure above shows one way of covering the tiles with the carpets such that no white tiles are visible.
Note that the carpets are able to overlap one another.

Constraints:

1 <= carpetLen <= floor.length <= 1000
floor[i] is either '0' or '1'.
1 <= numCarpets <= 1000

Asked at 1 company

Google

Topics

Hints open one at a time

Hint 1

Can you think of a DP solution?

Hint 2

Let DP[i][j] denote the minimum number of white tiles still visible from indices i to floor.length-1 after covering with at most j carpets.

Hint 3

The transition will be whether to put down the carpet at position i (if possible), or not.

17:07

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