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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>LC 141: Linked List Cycle - Algorithm Visualization</title>
<link rel="stylesheet" href="styles.css">
<script src="https://d3js.org/d3.v7.min.js"></script>
</head>
<body>
<div class="container">
<div class="problem-info">
<h1><span class="problem-number">#141</span> Linked List Cycle</h1>
<p>Given the head of a linked list, determine if there is a cycle in it. A cycle exists if some node can be reached again by following the next pointers.</p>
<div class="problem-meta">
<span class="meta-tag">🔗 Linked List</span>
<span class="meta-tag">🐢🐇 Floyd's Algorithm</span>
<span class="meta-tag">⏱️ O(n)</span>
<span class="meta-tag">💾 O(1)</span>
</div>
<div class="file-ref">
📄 Python: <code>python/0141_linked_list_cycle/0141_linked_list_cycle.py</code>
</div>
</div>
<div class="explanation-panel">
<h4>🧠 How It Works (Layman's Terms)</h4>
<p>Imagine two runners on a circular track - one slow (🐢 tortoise) and one fast (🐇 hare):</p>
<ul>
<li><strong>Slow pointer:</strong> Moves 1 step at a time</li>
<li><strong>Fast pointer:</strong> Moves 2 steps at a time</li>
<li><strong>If there's a cycle:</strong> Fast will eventually catch up and meet slow</li>
<li><strong>If no cycle:</strong> Fast will reach the end (null)</li>
<li><strong>Why it works:</strong> In a cycle, fast gains 1 step per iteration, so they must meet!</li>
</ul>
</div>
<div class="visualization-section">
<h3>🎬 Step-by-Step Visualization</h3>
<div class="controls">
<button class="btn btn-primary" id="stepBtn" onclick="step()">Step</button>
<button class="btn btn-success" id="autoBtn" onclick="toggleAuto()">Auto Run</button>
<button class="btn btn-warning" onclick="reset()">Reset</button>
</div>
<div class="info-box secondary" style="margin-bottom: 20px;">
🔗 List: <strong>[3 → 2 → 0 → -4] → (back to node 2)</strong> — Has a cycle!
</div>
<div class="status-message" id="statusMessage">
Click "Step" or "Auto Run" to start visualization
</div>
<div id="linkedListContainer" style="width: 100%; height: 350px; margin-top: 20px;"></div>
<div class="variable-section" style="margin: 20px 0; display: flex; gap: 30px; justify-content: center;">
<div class="variable" style="background: #e3f2fd;">
<span class="var-name">🐢 slow</span>
<span class="var-value" id="slowValue">3</span>
<span class="var-desc">moves 1 step</span>
</div>
<div class="variable" style="background: #fce4ec;">
<span class="var-name">🐇 fast</span>
<span class="var-value" id="fastValue">2</span>
<span class="var-desc">moves 2 steps</span>
</div>
<div class="variable">
<span class="var-name">Iteration</span>
<span class="var-value" id="iterValue">0</span>
</div>
</div>
</div>
<div class="code-section">
<h3>💻 Python Solution (Floyd's Tortoise and Hare)</h3>
<div class="code-block">
<pre>from typing import List, Optional
"""
LeetCode Linked List Cycle
Problem from LeetCode: https://leetcode.com/problems/linked-list-cycle/
Description:
Given head, the head of a linked list, determine if the linked list has a cycle in it.
There is a cycle in a linked list if there is some node in the list that can be reached again by continuously following the next pointer. Internally, pos is used to denote the index of the node that tail's next pointer is connected to. Note that pos is not passed as a parameter.
Return true if there is a cycle in the linked list. Otherwise, return false.
Example 1:
Input: head = [3,2,0,-4], pos = 1
Output: true
Explanation: There is a cycle in the linked list, where the tail connects to the 1st node (0-indexed).
Example 2:
Input: head = [1,2], pos = 0
Output: true
Explanation: There is a cycle in the linked list, where the tail connects to the 0th node.
Example 3:
Input: head = [1], pos = -1
Output: false
Explanation: There is no cycle in the linked list.
"""
class ListNode:
def __init__(self, x):
self.val = x
self.next = None
class Solution:
def has_cycle(self, head: Optional[ListNode]) -> bool:
"""
Determine if a linked list has a cycle using Floyd's Tortoise and Hare algorithm.
Args:
head: Head of the linked list
Returns:
bool: True if the linked list has a cycle, False otherwise
"""
if not head:
return False
slow = head
fast = head.next
while slow and fast:
if not fast or not fast.next:
return False
if fast == slow:
return True
slow = slow.next
fast = fast.next.next
return False
def has_cycle_hashset(self, head: Optional[ListNode]) -> bool:
"""
Determine if a linked list has a cycle using a hash set to track visited nodes.
O(n) time and space complexity.
Args:
head: Head of the linked list
Returns:
bool: True if the linked list has a cycle, False otherwise
"""
visited = set()
current = head
while current:
if current in visited:
return True
visited.add(current)
current = current.next
return False
# Helper function to create a linked list with a cycle
def create_cyclic_linked_list(arr, pos):
if not arr:
return None
head = ListNode(arr[0])
current = head
nodes = [head]
for val in arr[1:]:
current.next = ListNode(val)
current = current.next
nodes.append(current)
# Create cycle if pos is valid
if pos >= 0 and pos < len(nodes):
current.next = nodes[pos]
return head
if __name__ == '__main__':
# Example usage based on LeetCode sample
solution = Solution()
# Example 1
head1 = create_cyclic_linked_list([3, 2, 0, -4], 1)
result1 = solution.has_cycle(head1)
print(f"Example 1: {result1}") # Expected output: True
# Example 2
head2 = create_cyclic_linked_list([1, 2], 0)
result2 = solution.has_cycle(head2)
print(f"Example 2: {result2}") # Expected output: True
# Example 3
head3 = create_cyclic_linked_list([1], -1)
result3 = solution.has_cycle(head3)
print(f"Example 3: {result3}") # Expected output: False
# Compare with hash set approach
print("\nUsing hash set approach:")
head4 = create_cyclic_linked_list([3, 2, 0, -4], 1)
result4 = solution.has_cycle_hashset(head4)
print(f"Example 1: {result4}") # Expected output: True
</pre>
</div>
</div>
</div>
<script>
// Linked list: 3 -> 2 -> 0 -> -4 -> (back to 2)
const nodes = [
{ val: 3, id: 0 },
{ val: 2, id: 1 },
{ val: 0, id: 2 },
{ val: -4, id: 3 }
];
const cycleStart = 1; // Node index where cycle starts (node with value 2)
let slowIdx = 0;
let fastIdx = 1;
let iteration = 0;
let autoInterval = null;
let finished = false;
function getNextIdx(idx) {
if (idx === nodes.length - 1) {
return cycleStart; // Cycle back
}
return idx + 1;
}
function init() {
renderLinkedList();
updateVariables();
}
function renderLinkedList() {
const container = document.getElementById('linkedListContainer');
const width = container.offsetWidth;
const height = container.offsetHeight;
d3.select('#linkedListContainer').selectAll('*').remove();
const svg = d3.select('#linkedListContainer')
.append('svg')
.attr('width', width)
.attr('height', height);
// Position nodes in a shape that shows the cycle
const centerX = width / 2;
const centerY = height / 2;
const nodeRadius = 35;
// Create positions: 3 → 2 → 0 → -4 with -4 looping back to 2
const positions = [
{ x: centerX - 180, y: centerY - 50 }, // Node 0 (val: 3)
{ x: centerX - 60, y: centerY - 50 }, // Node 1 (val: 2) - cycle start
{ x: centerX + 60, y: centerY + 30 }, // Node 2 (val: 0)
{ x: centerX - 60, y: centerY + 110 } // Node 3 (val: -4)
];
// Draw arrows
const arrowHead = svg.append('defs').append('marker')
.attr('id', 'arrowhead')
.attr('viewBox', '0 0 10 10')
.attr('refX', 8)
.attr('refY', 5)
.attr('markerWidth', 6)
.attr('markerHeight', 6)
.attr('orient', 'auto')
.append('path')
.attr('d', 'M 0 0 L 10 5 L 0 10 Z')
.attr('fill', '#666');
// Regular arrows
for (let i = 0; i < nodes.length - 1; i++) {
const start = positions[i];
const end = positions[i + 1];
const angle = Math.atan2(end.y - start.y, end.x - start.x);
svg.append('line')
.attr('x1', start.x + nodeRadius * Math.cos(angle))
.attr('y1', start.y + nodeRadius * Math.sin(angle))
.attr('x2', end.x - nodeRadius * Math.cos(angle))
.attr('y2', end.y - nodeRadius * Math.sin(angle))
.attr('stroke', '#666')
.attr('stroke-width', 2)
.attr('marker-end', 'url(#arrowhead)');
}
// Cycle arrow (from -4 back to 2)
const lastPos = positions[3];
const cyclePos = positions[1];
// Draw curved arrow for cycle
svg.append('path')
.attr('d', `M ${lastPos.x - 20} ${lastPos.y - 20}
Q ${lastPos.x - 100} ${lastPos.y - 80}
${cyclePos.x - 20} ${cyclePos.y + 20}`)
.attr('fill', 'none')
.attr('stroke', '#e91e63')
.attr('stroke-width', 2)
.attr('stroke-dasharray', '5,5')
.attr('marker-end', 'url(#arrowhead)');
// Cycle label
svg.append('text')
.attr('x', lastPos.x - 100)
.attr('y', lastPos.y - 60)
.attr('fill', '#e91e63')
.attr('font-size', '12px')
.text('cycle!');
// Draw nodes
nodes.forEach((node, i) => {
const pos = positions[i];
const g = svg.append('g')
.attr('transform', `translate(${pos.x}, ${pos.y})`);
// Node circle
let fillColor = '#fff';
let strokeColor = '#667eea';
let strokeWidth = 3;
if (slowIdx === i && fastIdx === i) {
fillColor = '#ab47bc'; // Purple when both are here
strokeWidth = 5;
} else if (slowIdx === i) {
fillColor = '#2196f3'; // Blue for slow
strokeWidth = 5;
} else if (fastIdx === i) {
fillColor = '#e91e63'; // Pink for fast
strokeWidth = 5;
}
if (i === cycleStart) {
strokeColor = '#e91e63';
}
g.append('circle')
.attr('r', nodeRadius)
.attr('fill', fillColor)
.attr('stroke', strokeColor)
.attr('stroke-width', strokeWidth);
// Node value
g.append('text')
.attr('text-anchor', 'middle')
.attr('dy', 5)
.attr('font-size', '18px')
.attr('font-weight', 'bold')
.attr('fill', (slowIdx === i || fastIdx === i) ? '#fff' : '#333')
.text(node.val);
// Node index
g.append('text')
.attr('text-anchor', 'middle')
.attr('dy', -45)
.attr('font-size', '12px')
.attr('fill', '#666')
.text(`index: ${i}`);
// Pointer labels
if (slowIdx === i && fastIdx === i) {
g.append('text')
.attr('text-anchor', 'middle')
.attr('dy', 55)
.attr('font-size', '14px')
.attr('fill', '#ab47bc')
.text('🐢🐇 MEET!');
} else {
if (slowIdx === i) {
g.append('text')
.attr('text-anchor', 'middle')
.attr('dy', 55)
.attr('font-size', '14px')
.attr('fill', '#2196f3')
.text('🐢 slow');
}
if (fastIdx === i) {
g.append('text')
.attr('text-anchor', 'middle')
.attr('dy', fastIdx === slowIdx ? 75 : 55)
.attr('font-size', '14px')
.attr('fill', '#e91e63')
.text('🐇 fast');
}
}
});
// Legend
svg.append('circle').attr('cx', 30).attr('cy', 20).attr('r', 8).attr('fill', '#2196f3');
svg.append('text').attr('x', 45).attr('y', 24).text('slow (🐢)').attr('font-size', '12px');
svg.append('circle').attr('cx', 30).attr('cy', 45).attr('r', 8).attr('fill', '#e91e63');
svg.append('text').attr('x', 45).attr('y', 49).text('fast (🐇)').attr('font-size', '12px');
}
function updateVariables() {
document.getElementById('slowValue').textContent = nodes[slowIdx].val;
document.getElementById('fastValue').textContent = nodes[fastIdx].val;
document.getElementById('iterValue').textContent = iteration;
}
function step() {
if (finished) return;
iteration++;
// Check if they meet
if (slowIdx === fastIdx) {
finished = true;
document.getElementById('statusMessage').className = 'status-message success';
document.getElementById('statusMessage').textContent =
`✅ CYCLE DETECTED! Slow and fast pointers meet at node ${nodes[slowIdx].val}`;
document.getElementById('stepBtn').disabled = true;
stopAuto();
renderLinkedList();
updateVariables();
return;
}
// Move slow by 1
const oldSlow = slowIdx;
slowIdx = getNextIdx(slowIdx);
// Move fast by 2
const oldFast = fastIdx;
fastIdx = getNextIdx(fastIdx);
fastIdx = getNextIdx(fastIdx);
document.getElementById('statusMessage').textContent =
`Iteration ${iteration}: slow ${nodes[oldSlow].val} → ${nodes[slowIdx].val}, fast ${nodes[oldFast].val} → ${nodes[fastIdx].val}`;
renderLinkedList();
updateVariables();
// Check again after move
if (slowIdx === fastIdx) {
finished = true;
document.getElementById('statusMessage').className = 'status-message success';
document.getElementById('statusMessage').textContent =
`✅ CYCLE DETECTED! Slow and fast pointers meet at node ${nodes[slowIdx].val}`;
document.getElementById('stepBtn').disabled = true;
stopAuto();
}
}
function toggleAuto() {
if (autoInterval) {
stopAuto();
} else {
document.getElementById('autoBtn').textContent = 'Pause';
autoInterval = setInterval(() => {
if (finished) {
stopAuto();
} else {
step();
}
}, 1000);
}
}
function stopAuto() {
if (autoInterval) {
clearInterval(autoInterval);
autoInterval = null;
}
document.getElementById('autoBtn').textContent = 'Auto Run';
}
function reset() {
stopAuto();
slowIdx = 0;
fastIdx = 1;
iteration = 0;
finished = false;
document.getElementById('stepBtn').disabled = false;
document.getElementById('statusMessage').className = 'status-message';
document.getElementById('statusMessage').textContent = 'Click "Step" or "Auto Run" to start visualization';
init();
}
init();
</script>
</body>
</html>