From 439308c71554d3f553c2c9c73f6fb68641694a4c Mon Sep 17 00:00:00 2001
From: System Administrator <root@adarshs-MacBook-Air.local>
Date: Tue, 6 Jun 2023 20:16:28 +0530
Subject: [PATCH] hare and tortoise algoritm of cycle detection in a linked
 list

---
 .../hare-tortoise-algorithm/README.md         |  3 ++
 .../__test__/hareTortoise.test.js             | 36 +++++++++++++++++++
 .../hare-tortoise-algorithm/hareTortoise.js   | 21 +++++++++++
 3 files changed, 60 insertions(+)
 create mode 100644 src/algorithms/linked-list/hare-tortoise-algorithm/README.md
 create mode 100644 src/algorithms/linked-list/hare-tortoise-algorithm/__test__/hareTortoise.test.js
 create mode 100644 src/algorithms/linked-list/hare-tortoise-algorithm/hareTortoise.js

diff --git a/src/algorithms/linked-list/hare-tortoise-algorithm/README.md b/src/algorithms/linked-list/hare-tortoise-algorithm/README.md
new file mode 100644
index 00000000..735493a3
--- /dev/null
+++ b/src/algorithms/linked-list/hare-tortoise-algorithm/README.md
@@ -0,0 +1,3 @@
+# Floyd's Cycle Detection Algorithm (aka Hare and Tortoise Algorithm)
+Floyd algorithm for finding the cycles in a linked list is used to determine presence of a cycle in the linked list using constant space and linear time (i.e. space complexity = O(1) and time comoplexity = O(n), where n is number of nodes in the list).
+ The algorithm uses two pointers where one pointer moves a littile faster (the hare pointer). If at any point of traversal, the fast pointer meets the slow pointer, we can say that we have a cycle in the linked list. Conversly if the fast pointer hits a null, we have reached the end of list and no cycle is present.
diff --git a/src/algorithms/linked-list/hare-tortoise-algorithm/__test__/hareTortoise.test.js b/src/algorithms/linked-list/hare-tortoise-algorithm/__test__/hareTortoise.test.js
new file mode 100644
index 00000000..c566ae7d
--- /dev/null
+++ b/src/algorithms/linked-list/hare-tortoise-algorithm/__test__/hareTortoise.test.js
@@ -0,0 +1,36 @@
+import LinkedList from "../../../../data-structures/linked-list/LinkedList";
+import LinkedListNode from "../../../../data-structures/linked-list/LinkedListNode";
+import hareAndTortoise from "../hareTortoise";
+
+function getTail(linkedList){
+    let tail = linkedList.head;
+    while(tail.next){
+        tail=tail.next;
+    }
+    return tail;
+}
+describe('cycleDetection',()=>{
+    it('should be able to properly detect no cycles in a linked list',()=>{
+        let simpleLinkedList = new LinkedList();
+        simpleLinkedList
+            .append(1)
+            .append(2)
+            .append(3);
+        
+        const containsCycle = hareAndTortoise(simpleLinkedList);
+        expect(containsCycle).toEqual(false);
+    });
+    it('should detect a cycle in the linked list',()=>{
+        let cyclicLinkedList = new LinkedList();
+        cyclicLinkedList
+            .append(1)
+            .append(2)
+            .append(3)
+            .append(4);
+        const tail = getTail(cyclicLinkedList);
+        tail.next = cyclicLinkedList.head;
+        const containsCycle = hareAndTortoise(cyclicLinkedList);
+        expect(containsCycle).toEqual(true);
+    });
+
+})
diff --git a/src/algorithms/linked-list/hare-tortoise-algorithm/hareTortoise.js b/src/algorithms/linked-list/hare-tortoise-algorithm/hareTortoise.js
new file mode 100644
index 00000000..6b9d8b33
--- /dev/null
+++ b/src/algorithms/linked-list/hare-tortoise-algorithm/hareTortoise.js
@@ -0,0 +1,21 @@
+/**
+ * @param {LinkedList} linkedList
+ * @returns {boolean}
+ */
+
+export default function hareAndTortoise(linkedList){
+    let hare = linkedList.head;
+    let tortoise = linkedList.head;
+    while(hare && hare.next && hare.next.next){
+        hare = hare.next.next;
+        tortoise = tortoise.next;
+        //iterate till "hare" has not reached the end of list
+        if(hare == tortoise){
+            // we got a cycle
+            return true;
+        }
+        
+    }
+    // no cycle just the end of list
+    return false;
+}
\ No newline at end of file