maximize_the_confusion_of_an_exam.md

Solution - 1 Sliding Window

Code Explanation

1. The maxConsecutiveAnswers function takes an answerKey string and an integer k as input. It calculates the maximum consecutive answers by calling the flipper function twice, once for flipping 'F' and once for flipping 'T'. It returns the maximum count among the two results.

2. The flipper function takes the answerKey, k, and the character countLetter as input. It initializes variables max and count to keep track of the maximum consecutive count and the current count, respectively. It also uses a Queue called queue to store the indices of flipped answers.

3. The function iterates through the answerKey string using a for loop. For each character at index i, it checks if it matches the countLetter. If it does, the count is incremented.

4. If the character doesn't match countLetter, it checks if there are remaining flips (k > 0). If there are, it performs the flip by adding the index i to the queue, decrementing k, and incrementing the count.

5. If there are no remaining flips (k = 0), it means the window has reached its maximum size. It updates the max value by comparing the current count with the previous maximum. Then, it removes the first encountered index from the queue and calculates the new count by subtracting the removed index from the current index.

6. After the loop, it performs a final check to update max if the last window's count is greater than the current maximum.

7. The function returns the final max value.

Now, let's analyze the space and time complexity of the algorithm:

Space Complexity: The space complexity of the algorithm is as follows:

• The Queue used to store the indices of flipped answers can have a maximum size of k elements, depending on the number of allowed flips. Therefore, the space complexity of the Queue is O(k).
• The other variables (max, count, and letter) used in the algorithm require constant space, so they don't contribute significantly to the overall space complexity.

Hence, the overall space complexity is O(k), where k represents the maximum number of flips allowed.

Time Complexity: The time complexity of the algorithm is as follows:

• The algorithm iterates through the answerKey string once using a for loop. Since the loop runs n times, where n is the length of the answerKey, the time complexity of the loop is O(n).
• Within the loop, the operations performed, such as comparing characters, adding/removing elements from the Queue, and updating variables, all take constant time.

Therefore, the overall time complexity of the algorithm is O(n), where n represents the length of the input answerKey.

In summary, the space complexity is O(k), and the time complexity is O(n), where k represents the maximum number of flips allowed, and n represents the length of the answerKey.

import 'dart:collection';
import 'dart:math';

class Solution {
  int maxConsecutiveAnswers(String answerKey, int k) {
    return max(flipper(answerKey, k, 'F'), flipper(answerKey, k, 'T'));
  }

  int flipper(String answerKey, int k, String countLetter) {
    int maximum = 0;
    int count = 0;
    final Queue<int> queue = Queue<int>();
    for (int i = 0; i < answerKey.length; i++) {
      final String letter = answerKey[i];
      if (letter == countLetter)
        count++;
      else if (k > 0) {
        queue.add(i);
        k--;
        count++;
      } else {
        queue.add(i);
        maximum = max(count, maximum);
        final int firstEncountered = queue.removeFirst();
        count = i - firstEncountered;
      }
    }
    maximum = max(count, maximum);
    return maximum;
  }
}

Solution - 2 Linked List

Code Explanation

The given code implements a solution to find the maximum number of consecutive answers in an answer key, considering a maximum number of flips allowed. The maxConsecutiveAnswers function takes an answer key (a string of 'T' and 'F' representing true and false answers) and the maximum number of flips allowed (k), and returns the maximum number of consecutive answers after performing flips.

The implementation uses a custom LinkedList class to keep track of the indices where flips occur. The LinkedList class has a head and tail node, and it provides methods to add elements to the end of the list (add), remove the first element (removeFirst), and check if the list is empty (isEmpty).

The flipper function is a helper function used by maxConsecutiveAnswers. It iterates over the answer key and maintains a count of consecutive answers of the given countLetter (either 'T' or 'F'). If a different letter is encountered, it checks if there are any remaining flips (k > 0). If there are flips available, it adds the current index to the linkedList, decrements k, and increments the count. If there are no flips available, it adds the current index to the linkedList, updates the maximum count if necessary, removes the first encountered index from the linkedList, and calculates the new count based on the removed index.

Finally, the function returns the maximum count found.

Space Complexity

• The space complexity of the code is O(n), where n is the length of the answer key. This is because the LinkedList can store up to k indices, and in the worst case, if all indices require flips, the linkedList will contain k elements. Additionally, other variables like maximum, count, and letter require constant space.

Time Complexity

• The time complexity of the code is O(n), where n is the length of the answer key. This is because the code iterates over the answer key once, performing constant time operations like comparisons, additions, and removals in the linkedList. The operations performed on the linkedList are all O(1) since the implementation uses a singly linked list and keeps track of the tail node.

class Node {
 late int value;
  Node? next;

  Node(int value) {
    this.value = value;
    this.next = null;
  }
}

class LinkedList {
  Node? head;
  Node? tail;

  LinkedList() {
    head = null;
    tail = null;
  }

  void add(int value) {
    Node newNode = Node(value);
    if (head == null) {
      head = newNode;
      tail = newNode;
    } else {
      tail?.next = newNode;
      tail = newNode;
    }
  }

  int? removeFirst() {
    if (head == null) return null;
    int? value = head?.value;
    head = head?.next;
    if (head == null) tail = null;
    return value;
  }

  bool isEmpty() {
    return head == null;
  }
}

class Solution {
  int maxConsecutiveAnswers(String answerKey, int k) {
    return max(flipper(answerKey, k, 'F'), flipper(answerKey, k, 'T'));
  }

  int flipper(String answerKey, int k, String countLetter) {
    int maximum = 0;
    int count = 0;
    final LinkedList linkedList = LinkedList();
    for (int i = 0; i < answerKey.length; i++) {
      final String letter = answerKey[i];
      if (letter == countLetter)
        count++;
      else if (k > 0) {
        linkedList.add(i);
        k--;
        count++;
      } else {
        linkedList.add(i);
        maximum = max(count, maximum);
        final int? firstEncountered = linkedList.removeFirst();
        if (firstEncountered != null) {
          count = i - firstEncountered;
        }
      }
    }
    maximum = max(count, maximum);
    return maximum;
  }
}

Solution - 3

class Solution {
  int maxConsecutiveAnswers(String answerKey, int k) {
    int ans1 = solve(answerKey, k, 'T');
    int ans2 = solve(answerKey, k, 'F');
    return max(ans1, ans2);
  }

  int solve(String answerKey, int k, String c) {
    int i = 0;
    int j = 0;
    int count = 0;
    int n = answerKey.length;
    int answer = 0;
    while (j < n) {
      if (answerKey[j] == c) count++;
      while (i < n && count > k) {
        if (answerKey[i] == c) count--;
        i++;
      }
      answer = max(j - i + 1, answer);
      j++;
    }
    return answer;
  }
}