added floyd's algorithm

Linked_list/Floyd's_cycle_finding_algorithm/Detect_loop_or_cycle.c

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+#include <stdio.h>
+#include <stdlib.h>
+#include <stdbool.h>
+
+// Define the structure for a linked list node
+struct Node {
+    int data;              // Data part of the node
+    struct Node* next;     // Pointer to the next node
+};
+
+// Function to detect a loop in the linked list
+bool detectLoop(struct Node* head) {
+    // Initialize two pointers, slow and fast
+    struct Node *slow = head;  // Slow pointer moves one step
+    struct Node *fast = head;  // Fast pointer moves two steps
+
+    // Loop until we reach the end of the list
+    while (slow != NULL && fast != NULL && fast->next != NULL) {
+        slow = slow->next;           // Move slow one step
+        fast = fast->next->next;     // Move fast two steps
+
+        // If slow and fast meet, there is a loop
+        if (slow == fast) {
+            return true; // Loop detected
+        }
+    }
+    return false; // No loop
+}
+
+// Function to create a new linked list node
+struct Node* createNode(int data) {
+    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node)); // Allocate memory
+    newNode->data = data; // Set node data
+    newNode->next = NULL; // Initialize next pointer to NULL
+    return newNode;
+}
+
+int main() {
+    // Create a linked list: 10 -> 20 -> 30 -> 40 -> 50 -> 60
+    struct Node* head = createNode(10);
+    head->next = createNode(20);
+    head->next->next = createNode(30);
+    head->next->next->next = createNode(40);
+    head->next->next->next->next = createNode(50);
+    head->next->next->next->next->next = createNode(60);
+
+    // Create a loop for testing (linking the last node back to the third node)
+    head->next->next->next->next->next->next = head->next->next; // Creating a loop
+
+    // Check for loop in the linked list and print the result
+    if (detectLoop(head))
+        printf("Loop detected\n");
+    else
+        printf("No loop detected\n");
+
+    return 0; // End of the program
+}
+

Linked_list/Floyd's_cycle_finding_algorithm/readme.md

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+# Floyd's Cycle Finding Algorithm or Hare-Tortoise Algorithm
+It is a pointer algorithm that uses only two pointers.one pointer moves twice as fast as the other one.The faster one is called fast pointer and the other one is called slow pointer.
+
+While traversing the linked list one of these things will occur-
+1. The Fast pointer may reach the end (NULL) which shows that there is no loop in the linked list.
+2. The Fast pointer again catches the slow pointer at some time therefore a loop exists in the linked list.
+
+## why does Floyd’s Algorithm works?
+1. After each iteration where the slow pointer moves one step forward and the fast pointer moves two steps forward, the distance between the two pointers increases.
+2. Initially, if the slow pointer is at a distance k from a certain point in the cycle, then after one iteration, the distance between the slow and fast pointers becomes k+1.After two iterations, this distance becomes k+2 and so on.
+3. As they continue to move within the cycle, this distance will eventually equal the cycle length n.
+4. At this point, since the distance wraps around the cycle and both pointers are moving within the same cycle, they will meet.
+
+## Time Complexity
+O(n): The algorithm traverses the linked list at most twice. The first traversal is to determine if a loop exists Therefore, the time complexity is linear with respect to the number of nodes in the linked list.
+## Space Complexity
+O(1): The algorithm uses only two pointers (slow and fast), regardless of the size of the linked list. This means the space complexity is constant.
+
+## Example
+10 -> 20 -> 30 ->40 -> 50 -> 60->30
+here we can see the link part of data of 60 is connected to data of 30.therefore there is a loop.and this algorithm will detect it and prints loop detected.
+
+10 -> 20 -> 30 ->40->NULL
+here there is no loop and last node is connected to null which means the end of linked list.Therefore it prints no loop dected.
+
+
+