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<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April 15, 202502:32:08 UTC">April 15, 2025</span>&emsp;

<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="September 21, 202500:17:26 UTC">September 21, 2025</span>&emsp;

<p>Here we need to find out the point<strong>C</strong>, i.e the starting point of the cycle.</p>

<h2id="proposed-algorithm">Proposed algorithm<aclass="headerlink"href="#proposed-algorithm"title="Permanent link">&para;</a></h2>

<p>The algorithm is called<strong>Floyd’s Cycle Algorithm or Tortoise And Hare algorithm</strong>.

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.</p>

<h3id="step-1-presence-of-the-cycle">Step 1: Presence of the cycle<aclass="headerlink"href="#step-1-presence-of-the-cycle"title="Permanent link">&para;</a></h3>

<li><spanclass="arithmatex">$slow$</span> will move one step at a time.</li>

<li><spanclass="arithmatex">$fast$</span> will move two steps at a time. (twice as speed as<spanclass="arithmatex">$slow$</span> pointer).</li>

<li>Check if at any point they point to the same node before any one(or both) reach null.</li>

<li>If they point toany same node at any point of their journey, itwould indicatethatthe cycle indeed exists in the linked list.</li>

<li>If we get null, itwould indicate that the linked list has no cycle.</li>

<li>If they point tothe same node at any point of their journey, itindicatesthata cycle indeed exists in the linked list.</li>

<li>If we get null, itindicates that the linked list has no cycle.</li>

<divstyle="text-align: center;">

<imgsrc="tortoise_hare_cycle_found.png"alt=""Foundcycle"">

<p>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.,<strong>C</strong>.</p>

<p>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.,<strong>C</strong>.</p>

<h3id="step-2-starting-point-of-the-cycle">Step 2: Starting point of the cycle<aclass="headerlink"href="#step-2-starting-point-of-the-cycle"title="Permanent link">&para;</a></h3>

<li>Reset the<spanclass="arithmatex">$slow$</span> pointer to the<strong>head</strong> of the linked list.</li>

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