#2024

Medium

auto_awesomeBinary search over the valid answer space

LeetCode Problem Workspace

Maximize the Confusion of an Exam

Maximize the Confusion of an Exam requires adjusting at most k answers to create the longest consecutive true or false sequence efficiently.

string binary search sliding window prefix sum

Problem Statement

A teacher is preparing a true/false test represented as a string answerKey, where 'T' denotes true and 'F' denotes false. The goal is to increase confusion by creating the longest block of consecutive identical answers by flipping at most k answers from 'T' to 'F' or 'F' to 'T'.

Given answerKey and an integer k, determine the maximum number of consecutive 'T's or 'F's achievable after performing up to k flips. Each flip changes one answer, and the sequence must be optimized for length of identical consecutive characters.

Examples

Example 1

Input: answerKey = "TTFF", k = 2

Output: 4

We can replace both the 'F's with 'T's to make answerKey = "TTTT". There are four consecutive 'T's.

Example 2

Input: answerKey = "TFFT", k = 1

Output: 3

We can replace the first 'T' with an 'F' to make answerKey = "FFFT". Alternatively, we can replace the second 'T' with an 'F' to make answerKey = "TFFF". In both cases, there are three consecutive 'F's.

Example 3

Input: answerKey = "TTFTTFTT", k = 1

Output: 5

We can replace the first 'F' to make answerKey = "TTTTTFTT" Alternatively, we can replace the second 'F' to make answerKey = "TTFTTTTT". In both cases, there are five consecutive 'T's.

Constraints

n == answerKey.length
1 <= n <= 5 * 104
answerKey[i] is either 'T' or 'F'
1 <= k <= n

Solution Approach

Binary Search on Maximum Length

Use binary search to guess the possible maximum length of consecutive identical answers. For each candidate length, check if it is possible to achieve by flipping at most k characters using a helper sliding window function.

Sliding Window Validation

Maintain a window counting the number of characters needing flips to reach the candidate length. If the count exceeds k, shrink the window. If any window satisfies the flip constraint, the candidate length is feasible.

Optimizing Using Previous Maximums

Track the maximum consecutive identical characters seen so far and reuse it to prune unnecessary computations. This prevents re-scanning overlapping windows and leverages the insight from the binary search approach.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n log n) due to binary search over possible lengths and O(n) sliding window checks for each length. Space complexity is O(1) for counters and window indices, ignoring input storage.

What Interviewers Usually Probe

Look for a solution combining binary search with a sliding window over the answerKey.
Consider how previous window calculations can help determine feasibility of the current candidate length.
Check handling of edge cases where k is large enough to flip all answers or very small with alternating patterns.

Common Pitfalls or Variants

Common pitfalls

Failing to check both 'T' and 'F' as the target character when maximizing consecutive length.
Not shrinking the sliding window correctly when flips exceed k, leading to incorrect results.
Assuming consecutive maximum always starts at index 0, ignoring overlapping windows later.

Follow-up variants

Maximizing consecutive answers with multiple choice options instead of just T/F.
Finding the minimum flips needed to achieve a given consecutive length.
Applying the same binary search and sliding window approach to a circular exam string.

FAQ

What is the main strategy for Maximize the Confusion of an Exam?

Use binary search over possible consecutive lengths combined with sliding window checks to determine feasibility with at most k flips.

Do I need to consider both 'T' and 'F' when flipping?

Yes, each type must be evaluated separately since maximizing consecutive length may differ for 'T' and 'F'.

What is the time complexity for this approach?

The approach runs in O(n log n) time because each binary search candidate length requires an O(n) sliding window check.

Can this pattern be applied to other string flipping problems?

Yes, any problem involving maximizing consecutive identical characters with limited flips can use the binary search plus sliding window pattern.

What failure modes should I watch for in this problem?

Common issues include not handling overlapping windows correctly, ignoring one character type, and exceeding k flips in window validation.

terminal

Solution

Solution 1: Sliding Window

We design a function $\textit{f}(c)$, which represents the longest length of consecutive characters under the condition that at most $k$ characters $c$ can be replaced, where $c$ can be 'T' or 'F'. The answer is $\max(\textit{f}('T'), \textit{f}('F'))$.

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class Solution:
    def maxConsecutiveAnswers(self, answerKey: str, k: int) -> int:
        def f(c: str) -> int:
            cnt = l = 0
            for ch in answerKey:
                cnt += ch == c
                if cnt > k:
                    cnt -= answerKey[l] == c
                    l += 1
            return len(answerKey) - l

        return max(f("T"), f("F"))

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