Introduction

This C++ project implements a cycle detection algorithm for linked lists. The main focus is to determine if a given linked list contains a cycle, which occurs when a node's next pointer points to a previous node in the list. This is particularly useful in various computer science and data structure applications to avoid infinite loops and optimize memory usage.

Algorithms

1. Cycle Detection in Linked List

Logic

• The algorithm iterates through the linked list, using a hash set (std::unordered_set) to store and track the addresses of visited nodes. If a node is revisited (i.e., its address is already in the set), a cycle is detected.

Complexity Analysis

• Time Complexity: O(n), where n is the number of nodes in the linked list. Each node is visited at most once.
• Space Complexity: O(n), as additional space is required for the hash set storing the node addresses.

2. Linked List Construction

Logic

• Constructs a linked list from a vector of values and introduces a cycle at a specified index.

Complexity Analysis

• Time Complexity: O(n), primarily due to the list construction.
• Space Complexity: O(n), for storing the created nodes.

Code Snippet

bool hasCycle(ListNode* head) {
    if (head == nullptr || head->next == nullptr) { return false; }
    std::unordered_set<ListNode*> nodeList;
    while (head != nullptr) {
        bool result = (nodeList.insert(head)).second;
        if (!result) { return true; }
        head = head->next;
    }
    return false;
}

ListNode* buildCyclicalList(const std::vector<int>& values, int cycleIndex) {
	if (values.empty()) { return nullptr; }
	
	ListNode dummy(0);
	ListNode* current = &dummy;
	std::vector<ListNode*> nodes;

	for (int element : values) {
		current->next = new ListNode(element);
		current = current->next;
		nodes.push_back(current);
	}

	// Create a cycle by linking the tail to the node specified by the cycleIndex
	if (cycleIndex >= 0 && cycleIndex < values.size()) {
		current->next = nodes[cycleIndex];
	}

	return dummy.next;
}

void deleteList(ListNode* head) {
	while (head != nullptr) {
		ListNode* temp = head;
		head = head->next;
		delete temp;
	}
}

How to Use

1. Include the Necessary Files: Ensure that ListNode.h and the implementation files for the cycle detection algorithm are included in your project.

2. Create a Linked List: Utilize buildCyclicalList to create a linked list. You can specify node values and the position to introduce a cycle (if needed).

3. Detect a Cycle: Call hasCycle with your linked list as the argument to check for the presence of a cycle. The function returns true if a cycle is detected and false otherwise.

4. Memory Management: After testing, use deleteList to properly deallocate memory used by the linked list, especially if it's non-cyclical.