Sep 22, 2025 · Sep 10, 2025 · Sep 10, 2025 · Sep 10, 2025 · Sep 21, 2025
diff --git a/src/others/tortoise_and_hare.md b/src/others/tortoise_and_hare.md

 ## Proposed algorithm
 The algorithm is called **Floyd’s Cycle Algorithm or Tortoise And Hare algorithm**.
 In order to figure out the starting point of the cycle, we need to figure outof the thecycle even exists or not.
 So, it involved two steps:
 In order to figure out the starting point of the cycle, we need to figure outif acycle even exists.
 This involves two steps:
 1. Figure out the presence of the cycle.
 2. Find out the starting point of the cycle.

 3. $slow$ will move one step at a time.
 4. $fast$ will move two steps at a time. (twice as speed as $slow$ pointer).
 5. Check if at any point they point to the same node before any one(or both) reach null.
 6. If they point toany same node at any point of their journey, itwould indicatethatthe cycle indeed exists in the linked list.
 7. If we get null, itwould indicate that the linked list has no cycle.
 6. If they point tothe same node at any point of their journey, itindicatesthata cycle indeed exists in the linked list.
 7. If we get null, itindicates that the linked list has no cycle.

 <div style="text-align: center;">
  <img src="tortoise_hare_cycle_found.png" alt=""Found cycle"">
 </div>

 Now, that we have figured outthat there is a cycle present in the linked list, for the next step we need to find out the starting point of cycle, i.e., **C**.
 Now, that we have figured outif there is a cycle present in the linked list, for the next step we need to find out the starting point of cycle, i.e., **C**.
 ### Step 2: Starting point of the cycle
 1. Reset the $slow$ pointer to the **head** of the linked list.
 2. Move both pointers one step at a time.
Original file line number	Diff line number	Diff line change
Expand Up		@@ -15,8 +15,8 @@ Here we need to find out the point C, i.e the starting point of the cycle.

		## Proposed algorithm
		The algorithm is called Floyd’s Cycle Algorithm or Tortoise And Hare algorithm.
		In order to figure out the starting point of the cycle, we need to figure outof the thecycle even exists or not.
		So, it involved two steps:
		In order to figure out the starting point of the cycle, we need to figure outif acycle even exists.
		This involves two steps:
		1. Figure out the presence of the cycle.
		2. Find out the starting point of the cycle.

Expand All		@@ -26,14 +26,14 @@ So, it involved two steps:
		3. $slow$ will move one step at a time.
		4. $fast$ will move two steps at a time. (twice as speed as $slow$ pointer).
		5. Check if at any point they point to the same node before any one(or both) reach null.
		6. If they point toany same node at any point of their journey, itwould indicatethatthe cycle indeed exists in the linked list.
		7. If we get null, itwould indicate that the linked list has no cycle.
		6. If they point tothe same node at any point of their journey, itindicatesthata cycle indeed exists in the linked list.
		7. If we get null, itindicates that the linked list has no cycle.

		<div style="text-align: center;">
		<img src="tortoise_hare_cycle_found.png" alt=""Found cycle"">
		</div>

		Now, that we have figured outthat there is a cycle present in the linked list, for the next step we need to find out the starting point of cycle, i.e., C.
		Now, that we have figured outif there is a cycle present in the linked list, for the next step we need to find out the starting point of cycle, i.e., C.
		### Step 2: Starting point of the cycle
		1. Reset the $slow$ pointer to the head of the linked list.
		2. Move both pointers one step at a time.
Expand Down