#2379

Easy

auto_awesomeSliding window with running state updates

LeetCode Problem Workspace

Minimum Recolors to Get K Consecutive Black Blocks

Given a string of blocks, determine the minimum number of recolors needed to get k consecutive black blocks.

Problem Statement

You are given a string blocks of length n, where each character is either 'W' (white) or 'B' (black). The string represents a series of blocks, and you are asked to determine the minimum number of recoloring operations required to make k consecutive blocks black.

In each operation, you can recolor one 'W' block to a 'B' block. Your goal is to achieve at least k consecutive black blocks, minimizing the number of recolors needed. You must implement a solution that efficiently finds this result.

Examples

Example 1

Input: blocks = "WBBWWBBWBW", k = 7

Output: 3

One way to achieve 7 consecutive black blocks is to recolor the 0th, 3rd, and 4th blocks so that blocks = "BBBBBBBWBW". It can be shown that there is no way to achieve 7 consecutive black blocks in less than 3 operations. Therefore, we return 3.

Example 2

Input: blocks = "WBWBBBW", k = 2

Output: 0

No changes need to be made, since 2 consecutive black blocks already exist. Therefore, we return 0.

Constraints

n == blocks.length
1 <= n <= 100
blocks[i] is either 'W' or 'B'.
1 <= k <= n

Solution Approach

Sliding Window Technique

Use a sliding window of size k to traverse through the string. For each window, count the number of 'W' blocks, which are the blocks that need to be recolored. By sliding the window from left to right, we can efficiently track and update the count of white blocks within the current window.

Updating Window with Running State

As the window slides, adjust the count of white blocks by removing the effect of the block that is leaving the window and adding the effect of the block that is entering the window. This running state allows for a time complexity of O(n), optimizing the process of finding the minimal recolors.

Optimization by Minimizing Recolors

By iterating over all possible consecutive substrings of length k, the solution ensures that the minimum number of recolors is found. The result is the smallest number of 'W' blocks encountered within any k-length window.

Complexity Analysis

Metric	Value
Time	O(N)
Space	O(1)

The time complexity is O(n) because the solution uses a sliding window of size k that moves from left to right, updating the count in constant time for each position. The space complexity is O(1), as the algorithm only requires a constant amount of additional space to track the count of 'W' blocks within the window.

What Interviewers Usually Probe

Candidates should be able to recognize that a sliding window approach is optimal for this problem.
Watch for the ability to efficiently update the window state with minimal overhead as the window slides.
Look for candidates who can quickly explain the efficiency of the O(n) time complexity and O(1) space complexity.

Common Pitfalls or Variants

Common pitfalls

Not recognizing that the problem can be solved with a sliding window, leading to inefficient brute force approaches.
Failing to update the window's state efficiently as it slides, causing unnecessary recalculations.
Misunderstanding the constraints and not considering that the window must be exactly size k, potentially leading to incorrect results.

Follow-up variants

Consider variations where k is larger or smaller relative to n, or the string is heavily biased toward one color.
What if the problem asked for at least m consecutive black blocks, where m is variable and provided as an input?
Instead of counting 'W' blocks, what if the problem required finding the most efficient way to create exactly k consecutive black blocks without exceeding it?

FAQ

How can I solve the Minimum Recolors to Get K Consecutive Black Blocks problem?

Use the sliding window technique to efficiently count 'W' blocks in each k-length substring. Minimize recolors by finding the window with the fewest white blocks.

What is the time complexity of this problem?

The time complexity is O(n), as the sliding window only needs to traverse the string once and update the count in constant time.

Why is a sliding window approach the best method for this problem?

A sliding window minimizes redundant work by efficiently maintaining the count of 'W' blocks within each window, leading to an optimal O(n) time complexity.

What is the space complexity of the Minimum Recolors to Get K Consecutive Black Blocks problem?

The space complexity is O(1), as the solution only requires a constant amount of additional space to track the window state.

Can this problem be solved using brute force?

While brute force could work, it would be inefficient with a time complexity of O(n * k). The sliding window approach is much more optimal with O(n) time.

terminal

Solution

Solution 1: Sliding Window

We observe that what the problem actually asks for is the minimum number of white blocks in a sliding window of size $k$.

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class Solution:
    def minimumRecolors(self, blocks: str, k: int) -> int:
        ans = cnt = blocks[:k].count('W')
        for i in range(k, len(blocks)):
            cnt += blocks[i] == 'W'
            cnt -= blocks[i - k] == 'W'
            ans = min(ans, cnt)
        return ans

Continue Practicing

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