Cycle Detection
Detailed guide and Python implementation for the 'Cycle Detection' problem.
1. Concept Overview
The 'Cycle Detection' problem is a key challenge in the Graphs section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Cycle Detection.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Cycle Detection carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function has_cycle(graph) that takes a directed graph represented as an adjacency list of neighbor lists and returns True if it contains at least one cycle, or False otherwise.
- •1 <= V <= 500
- •0 <= E <= 1000
Examples
graph = {0: [1], 1: [2], 2: [0]}True
The path 0 -> 1 -> 2 -> 0 forms a cycle.
graph = {0: [1], 1: [2], 2: []}False
The graph is acyclic.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def has_cycle_bfs(num_nodes, edges):
from collections import deque
adj = [[] for _ in range(num_nodes)]
in_degree = [0] * num_nodes
for u, v in edges:
adj[u].append(v)
in_degree[v] += 1
queue = deque([i for i in range(num_nodes) if in_degree[i] == 0])
count = 0
while queue:
u = queue.popleft()
count += 1
for v in adj[u]:
in_degree[v] -= 1
if in_degree[v] == 0: queue.append(v)
return count != num_nodesBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def has_cycle_dfs(graph):
visited = set()
path = set()
def dfs(u):
visited.add(u)
path.add(u)
for v in graph[u]:
if v in path: return True
if v not in visited:
if dfs(v): return True
path.remove(u)
return False
for node in graph:
if node not in visited:
if dfs(node): return True
return FalseAlgorithm Pattern Checklist
When dealing with Graphs data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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