Graph Valid Tree
Decide whether an undirected graph is one connected acyclic tree.
Why does this pattern fit?
Restate the exact job
Decide whether an undirected graph is one connected acyclic tree.
A tree with n nodes has n − 1 edges and one component.
O(V + E) time · O(V) space
Checking only connectivity misses cycles; checking only edge count misses disconnection.
How to solve Graph Valid Tree
The goal is to solve this problem from the pattern, not to memorize a finished answer. Use this as a check after your own attempt.
What the question asks
Decide whether an undirected graph is one connected acyclic tree.
Why Graphs: traversal & ordering fits
A tree with n nodes has n − 1 edges and one component.
State to maintain
Edge count plus traversal/union state.
Transition
Reject wrong edge count, then verify all nodes connect without a repeated union.
Time and space
O(V + E) time · O(V) space
Counterexample to the tempting mistake
Checking only connectivity misses cycles; checking only edge count misses disconnection.
Prove it again tomorrow
Close this page. Rebuild the state and transition from memory, write a test that exposes the mistake above, then solve a fresh input without looking back. A same-day reread is practice, not proof of retention.