Leetcode #2477: Minimum Fuel Cost to Report to the Capital
In this guide, we solve Leetcode #2477 Minimum Fuel Cost to Report to the Capital in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is a tree (i.e., a connected, undirected graph with no cycles) structure country network consisting of n cities numbered from 0 to n - 1 and exactly n - 1 roads. The capital city is city 0.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Tree, Depth-First Search, Breadth-First Search, Graph
Intuition
The data forms a graph, so we should explore nodes and edges systematically.
A traversal ensures we visit each node once while maintaining the needed state.
Approach
Build an adjacency list and traverse with BFS or DFS.
Aggregate results as you visit nodes.
Steps:
- Build the graph.
- Traverse with BFS/DFS.
- Accumulate the required output.
Example
Input: roads = [[0,1],[0,2],[0,3]], seats = 5
Output: 3
Explanation:
- Representative1 goes directly to the capital with 1 liter of fuel.
- Representative2 goes directly to the capital with 1 liter of fuel.
- Representative3 goes directly to the capital with 1 liter of fuel.
It costs 3 liters of fuel at minimum.
It can be proven that 3 is the minimum number of liters of fuel needed.
Python Solution
class Solution:
def minimumFuelCost(self, roads: List[List[int]], seats: int) -> int:
def dfs(a: int, fa: int) -> int:
nonlocal ans
sz = 1
for b in g[a]:
if b != fa:
t = dfs(b, a)
ans += ceil(t / seats)
sz += t
return sz
g = defaultdict(list)
for a, b in roads:
g[a].append(b)
g[b].append(a)
ans = 0
dfs(0, -1)
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.