Welcome back! As we advance in mastering interview-oriented problems using linked lists in C++, we will tackle practical algorithmic challenges that reflect real-world scenarios. These exercises are curated to enhance your problem-solving skills with linked lists using C++ as your tool of choice.

Imagine you're managing a digital library where some books are duplicated. Your goal is to identify and remove these duplicates to ensure each title is unique in your catalog.

A straightforward approach would be to compare each book with every other one in a nested loop fashion. While this method is easy to understand, it is inefficient with a time complexity of $O(n^2)$. Processing time increases significantly with larger lists, making this approach impractical for sizable datasets.

To overcome the inefficiencies of the naive approach, we utilize a more effective method using std::unordered_set in C++. This approach keeps track of unique titles as they're encountered, reducing the time complexity to $O(n)$. It is akin to maintaining a checklist, marking off books as they're cataloged, providing rapid lookup to ensure uniqueness.

Let's implement this strategy in C++:

C++
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1#include <unordered_set>
2#include <iostream>
3
4struct ListNode {
5    int value;
6    ListNode* next;
7    ListNode(int x) : value(x), next(nullptr) {}
8};
9
10class LinkedListChallenges {
11public:
12    ListNode* removeDuplicates(ListNode* head) {
13        if (head == nullptr || head->next == nullptr) {
14            return head; // No duplicates possible.
15        }
16        
17        std::unordered_set<int> seenBooks;
18        ListNode* current = head;
19        seenBooks.insert(current->value);
20
21        while (current->next != nullptr) {
22            if (seenBooks.find(current->next->value) != seenBooks.end()) {
23                // Duplicate found, remove it by deleting the node and adjusting the pointer.
24                ListNode* duplicateNode = current->next;
25                current->next = current->next->next;
26                delete duplicateNode;
27            } else {
28                // Unique entry, add to the set and proceed.
29                seenBooks.insert(current->next->value);
30                current = current->next;
31            }
32        }
33        return head; // Return modified list without duplicates.
34    }
35};

This C++ code defines a function to remove duplicate nodes from a linked list using an std::unordered_set to track encountered values. It starts by checking if the list is valid, then iterates through the list, checking if each node's value is already in the set of seen values. If a value is duplicate, the node is skipped by adjusting the pointer, otherwise, it's added to the set for future comparisons.

Consider a scenario involving a long-distance race where performance at every third checkpoint needs analysis. The linked list represents checkpoint times, and our task is to compute the average time at these checkpoints.

This task involves traversing the linked list while methodically tracking the sum and count of every third element, allowing us to calculate the desired average efficiently.

Let's translate this strategy into C++:

C++
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1#include <iostream>
2
3class LinkedListChallenges {
4public:
5    double averageOfEveryThird(ListNode* head) {
6        if (head == nullptr || head->next == nullptr || head->next->next == nullptr) {
7            return 0.0; // Not enough elements for averaging.
8        }
9
10        int sum = 0;
11        int count = 0;
12        ListNode* current = head;
13
14        for (int index = 1; current != nullptr; current = current->next, index++) {
15            if (index % 3 == 0) {
16                sum += current->value;
17                count++;
18            }
19        }
20        
21        return (double)sum / count; // Calculate and return the average.
22    }
23};

This C++ implementation aligns with our problem-solving strategy, capturing key details such as using a loop to tally every third element and computing their average with straightforward arithmetic.

Through this lesson, we explored optimization techniques for common linked list problems using C++. We examined efficient algorithms, emphasizing the importance of practical coding solutions that are optimized for technical interviews. By traversing from theory to practice, you can now apply these C++ strategies to develop scalable solutions effectively. It's your turn to practice, refine, and embed these skills, strengthening your C++ expertise for future challenges.