How do you solve Collect Coins in a Tree on LeetCode?

Collect Coins in a Tree (LeetCode #2603) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Pruning the tree by removing unnecessary nodes can significantly reduce the problem's complexity.

What is the brute force solution for Collect Coins in a Tree?

The brute force approach for Collect Coins in a Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we can explore all possible starting points in the tree and calculate the total distance required to collect all coins and return to the starting point. This method is straightforward but inefficient as it checks every possible path. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Collect Coins in a Tree?

Collect Coins in a Tree uses the following concepts: Array, Tree, Graph Theory, Topological Sort. The recommended patterns to study are: Graph Traversal (DFS, BFS), Tree Pruning, Dynamic Programming (for more complex variations).

What are the interview tips for Collect Coins in a Tree?

Always think about edge cases, such as trees with no coins or all coins at leaves. Explain your thought process clearly when discussing your approach to the interviewer. Practice DFS and BFS traversal techniques, as they are commonly used in tree and graph problems.

What are common mistakes when solving Collect Coins in a Tree?

Failing to recognize and remove redundant nodes (leaves without coins). Not considering the need to return to the starting point when calculating distances.

#2603

Collect Coins in a Tree

Hard

ArrayTreeGraph TheoryTopological SortGraph Traversal (DFS, BFS)Tree PruningDynamic Programming (for more complex variations)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution focuses on pruning the tree by removing unnecessary nodes (leaves without coins) and calculating the minimum distance needed to collect all coins efficiently. This reduces the number of nodes we need to traverse.

⚙️

Algorithm

3 steps

1Step 1: Build the graph from the edges.
2Step 2: Remove all leaves that do not have coins until no such leaves remain.
3Step 3: Perform a DFS from any remaining node to calculate the total distance needed to collect all coins and return.

solution.py28 lines

1# Full working Python code
2from collections import defaultdict, deque
3
4def collect_coins_optimal(coins, edges):
5    graph = defaultdict(list)
6    for a, b in edges:
7        graph[a].append(b)
8        graph[b].append(a)
9
10    leaves = deque([i for i in range(len(coins)) if coins[i] == 0])
11    while leaves:
12        leaf = leaves.popleft()
13        for neighbor in graph[leaf]:
14            graph[neighbor].remove(leaf)
15            if len(graph[neighbor]) == 1 and coins[neighbor] == 0:
16                leaves.append(neighbor)
17        graph.pop(leaf, None)
18
19    if not graph:
20        return 0
21
22    def dfs(node):
23        total_distance = 0
24        for neighbor in graph[node]:
25            total_distance += dfs(neighbor) + 1
26        return total_distance
27
28    return 2 * dfs(next(iter(graph)))

ℹ

Complexity note: The complexity is linear because we traverse each node and edge a constant number of times during the leaf removal and DFS traversal.

1Pruning the tree by removing unnecessary nodes can significantly reduce the problem's complexity.
2Understanding how to traverse trees efficiently is crucial for solving problems involving graphs.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.