How do you solve Minimum Fuel Cost to Report to the Capital on LeetCode?

Minimum Fuel Cost to Report to the Capital (LeetCode #2477) 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: Understanding the tree structure helps in visualizing the representatives' paths to the capital.

What is the brute force solution for Minimum Fuel Cost to Report to the Capital?

The brute force approach for Minimum Fuel Cost to Report to the Capital is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves calculating the total fuel needed for each representative to reach the capital individually. This method is straightforward but inefficient as it doesn't consider car pooling. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Fuel Cost to Report to the Capital?

Minimum Fuel Cost to Report to the Capital uses the following concepts: Tree, Depth-First Search, Breadth-First Search, Graph Theory. The recommended patterns to study are: Depth-First Search, Tree Traversal, Graph Theory.

What are the interview tips for Minimum Fuel Cost to Report to the Capital?

Always clarify the problem requirements and constraints before diving into the solution. Think about edge cases, such as when all representatives are in one city. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Minimum Fuel Cost to Report to the Capital?

Failing to account for the number of seats when calculating the number of cars needed. Not using DFS effectively to traverse the tree and gather representative counts.

#2477

Minimum Fuel Cost to Report to the Capital

Medium

TreeDepth-First SearchBreadth-First SearchGraph TheoryDepth-First SearchTree TraversalGraph Theory

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 uses a depth-first search (DFS) to calculate the size of each subtree. By knowing how many representatives are in each subtree, we can efficiently calculate the minimum number of cars needed to transport them to the capital.

⚙️

Algorithm

4 steps

1Step 1: Build a graph from the roads input.
2Step 2: Use DFS to calculate the size of each subtree rooted at each city.
3Step 3: For each subtree, calculate the number of cars needed based on the number of representatives and seats available.
4Step 4: Sum the total fuel costs for all representatives to reach the capital.

solution.py32 lines

1# Full working Python code
2from collections import defaultdict
3
4def minFuelCost(roads, seats):
5    graph = defaultdict(list)
6    for a, b in roads:
7        graph[a].append(b)
8        graph[b].append(a)
9
10    def dfs(node, parent):
11        total_representatives = 1  # Count this node as a representative
12        for neighbor in graph[node]:
13            if neighbor != parent:
14                total_representatives += dfs(neighbor, node)
15        return total_representatives
16
17    total_fuel = 0
18    def dfsFuel(node, parent):
19        nonlocal total_fuel
20        total_representatives = 1  # Count this node as a representative
21        for neighbor in graph[node]:
22            if neighbor != parent:
23                reps = dfsFuel(neighbor, node)
24                total_fuel += (reps + seats - 1) // seats
25                total_representatives += reps
26        return total_representatives
27
28    dfsFuel(0, -1)
29    return total_fuel
30
31# Example usage:
32print(minFuelCost([[0,1],[0,2],[0,3]], 5))  # Output: 3

ℹ

Complexity note: The time complexity is O(n) because we traverse each node once during the DFS. The space complexity is O(n) due to the storage of the graph and the recursion stack.

1Understanding the tree structure helps in visualizing the representatives' paths to the capital.
2Calculating the size of each subtree allows for efficient car pooling.

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