Collect Coins in a Tree
Time O(n) · Space O(n) · Official statement on LeetCode
Solutions
// Time: O(n)
// Space: O(n)
// tree, bfs
class Solution {
public:
int collectTheCoins(vector<int>& coins, vector<vector<int>>& edges) {
static const int DISTANCE = 2;
vector<unordered_set<int>> adj(size(coins));
for (const auto& e : edges) {
adj[e[0]].emplace(e[1]);
adj[e[1]].emplace(e[0]);
}
int n = size(coins);
for (int i = 0; i < size(coins); ++i) {
int u = i;
while (size(adj[u]) == 1 && !coins[u]) {
const int v = *cbegin(adj[u]);
adj[u].erase(v);
adj[v].erase(u);
--n;
u = v;
}
}
vector<int> q;
for (int u = 0; u < size(coins); ++u) {
if (size(adj[u]) == 1) {
q.emplace_back(u);
}
}
for (int _ = 0; _ < DISTANCE; ++_) {
vector<int> new_q;
for (const auto& u : q) {
if (empty(adj[u])) {
assert(n == 1);
break;
}
const int v = *cbegin(adj[u]);
adj[u].erase(v);
adj[v].erase(u);
--n;
if (size(adj[v]) == 1) {
new_q.emplace_back(v);
}
}
q = move(new_q);
}
return (n - 1) * 2;
}
};
Beginner Explanation
What is Collect Coins in a Tree?
Collect Coins in a Tree (LeetCode #2603) is a Hard problem that primarily trains breadth first search.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with tree and queue bfs.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold. Official solution notes mention: Tree, BFS.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Collect Coins in a Tree
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to tree and queue bfs.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n)) and space (O(n)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n) time and O(n) space.
Pattern focus: tree and queue bfs
Use the pattern as a checklist:
- tree — confirm the invariant holds after each step
- queue bfs — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n) |
| Space | O(n) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Collect Coins in a Tree
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for tree and queue bfs — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to tree and queue bfs:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: breadth first search.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Collect Coins in a Tree in a second language (cpp, python).
- Drill 3–5 more problems tagged breadth first search.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the tree and queue bfs approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Collect Coins in a Tree (#2603) — Hard. Pattern: tree and queue bfs. Complexity: O(n) time / O(n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Collect Coins in a Tree?+
The reference solutions aim for O(n) time and O(n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Collect Coins in a Tree use?+
It primarily maps to tree and queue bfs, within the broader topic of breadth first search.
Is Collect Coins in a Tree good for interviews?+
Yes — as a Hard problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/collect-coins-in-a-tree/