Why Floyd's Loop Detection Algorithm works ?

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Find First Element of Loop in Linked List

C++ Code:

void find_loop_beginning(Node *head){

    Node *slow = head;

    Node *fast = head;

    if (!head || !(head->next))

        return;

    while(slow && fast && fast->next){

        slow = slow->next;

        fast = fast->next->next;

        if(slow == fast)

            break;

    }

    

    // No Loop exixts

    if (slow != fast){

        std::cout << "No Loop" << std::endl;

        return;

    }

    

    // When Loop exists

    slow = head;

    while(slow != fast){

        slow = slow->next;

        fast = fast->next;

    }

    std::cout << "First loop element = " << slow->data << std::endl;

}

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Find k-th node from end in Linked List

void print_kth_from_end(Node *head, int k){

    Node *lead = head;

    Node *lag = head;

    while(k > 0){

        if(lead){

            k--;

            lead = lead->next;

        }

        else{

            std::cout << "K is larger than length of Linked List" << std::endl;

            return;

        }

    }

    while(lead){

        lead = lead->next;

        lag = lag->next;

    }

    std::cout << "kth node from end = " << lag->data << std::endl;

}

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Find the middle element of a Linked List

void print_middle(Node *head){

    Node *fast = head;

    Node *slow = head;

    while(fast && fast->next){

        fast = fast->next->next;

        slow = slow->next;

    }

    std::cout << slow->data << std::endl;

}

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Detect Loop in a Linked List

Method 1: (Hashing)

bool detect_loop_map(Node *head){

    std::unordered_map<Node*, bool> visited;

    Node *curr = head;

    while(curr){

        if (visited[curr] == true)

            return true;

        visited[curr] = true;

        curr = curr->next;

    }

    return false;

}

Method 2:(Floyd's Cycle Detection)

bool detect_loop_floyd(Node *head){

    Node *slow = head;

    Node *fast = head;

    while(slow && fast && fast->next){

        slow = slow->next;

        fast = fast->next->next;

        if (slow == fast){

            return true;

        }

    }

    return false;

}

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