Graph Valid Tree
Detailed guide and Python implementation for the 'Graph Valid Tree' problem.
1. Concept Overview
The 'Graph Valid Tree' problem is a key challenge in the Graphs section.
This implementation focuses on medium-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 Graph Valid Tree.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Graph Valid Tree 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
You have a graph of n nodes labeled from 0 to n - 1. You are given an integer n and a list of edges where edges[i] = [ai, bi] indicates that there is an undirected edge between nodes ai and bi in the graph.
Return True if the edges of the given graph make up a valid tree, and False otherwise.
Write a function validTree(n: int, edges: List[List[int]]) -> bool.
- •1 <= n <= 2000
- •0 <= len(edges) <= 5000
- •edges[i].length == 2
- •0 <= ai, bi < n
Examples
n = 5, edges = [[0,1],[0,2],[0,3],[1,4]]
True
The graph is fully connected and contains no cycles, so it is a valid tree.
n = 5, edges = [[0,1],[1,2],[2,3],[1,3],[1,4]]
False
The graph contains a cycle 1-2-3-1, so it is not a valid tree.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
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 is_valid_tree_opt(n, edges):
if len(edges) != n - 1: return False
par = [i for i in range(n)]
def find(n):
while n != par[n]: n = par[n]
return n
def union(n1, n2):
p1, p2 = find(n1), find(n2)
if p1 == p2: return False
par[p1] = p2
return True
for n1, n2 in edges:
if not union(n1, n2): return False
return TrueBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def is_valid_tree_brute(n, edges):
if not n: return True
adj = {i: [] for i in range(n)}
for n1, n2 in edges:
adj[n1].append(n2)
adj[n2].append(n1)
visit = set()
def dfs(i, prev):
if i in visit: return False
visit.add(i)
for j in adj[i]:
if j == prev: continue
if not dfs(j, i): return False
return True
return dfs(0, -1) and len(visit) == nAlgorithm Pattern Checklist
When dealing with Graphs data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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