Introduction

In this blog post, we will explore how to solve the LeetCode problem "2477" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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. You are given a 2D integer array roads where roads[i] = [ai, bi] denotes that there exists a bidirectional road connecting cities ai and bi. There is a meeting for the representatives of each city. The meeting is in the capital city. There is a car in each city. You are given an integer seats that indicates the number of seats in each car. A representative can use the car in their city to travel or change the car and ride with another representative. The cost of traveling between two cities is one liter of fuel. Return the minimum number of liters of fuel to reach the capital city. Example 1: 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. Example 2: Input: roads = [[3,1],[3,2],[1,0],[0,4],[0,5],[4,6]], seats = 2 Output: 7 Explanation: - Representative2 goes directly to city 3 with 1 liter of fuel. - Representative2 and representative3 go together to city 1 with 1 liter of fuel. - Representative2 and representative3 go together to the capital with 1 liter of fuel. - Representative1 goes directly to the capital with 1 liter of fuel. - Representative5 goes directly to the capital with 1 liter of fuel. - Representative6 goes directly to city 4 with 1 liter of fuel. - Representative4 and representative6 go together to the capital with 1 liter of fuel. It costs 7 liters of fuel at minimum. It can be proven that 7 is the minimum number of liters of fuel needed. Example 3: Input: roads = [], seats = 1 Output: 0 Explanation: No representatives need to travel to the capital city. Constraints: 1 <= n <= 105 roads.length == n - 1 roads[i].length == 2 0 <= ai, bi < n ai != bi roads represents a valid tree. 1 <= seats <= 105

Explanation

Here's the breakdown of the approach, complexities, and the Python code:

• High-Level Approach:

  • Represent the road network as an adjacency list to efficiently traverse the tree.
  • Perform Depth-First Search (DFS) starting from the capital (city 0) to calculate the number of representatives from each city that need to travel to the capital.
  • During DFS, calculate the fuel needed for each edge based on the number of representatives and the car capacity (seats).

• Complexity Analysis:

  • Runtime Complexity: O(N), where N is the number of cities.
  • Storage Complexity: O(N), primarily due to the adjacency list and the recursion stack during DFS.

Code

    from collections import defaultdict

def minimumFuelCost(roads, seats):
    n = len(roads) + 1
    adj = defaultdict(list)
    for u, v in roads:
        adj[u].append(v)
        adj[v].append(u)

    total_fuel = 0
    visited = [False] * n

    def dfs(city):
        nonlocal total_fuel
        visited[city] = True
        representatives = 1  # Start with the representative from the current city

        for neighbor in adj[city]:
            if not visited[neighbor]:
                reps = dfs(neighbor)
                representatives += reps
                total_fuel += (reps + seats - 1) // seats  # Calculate fuel needed for this edge

        return representatives

    visited[0] = True  # Mark the capital as visited to avoid cycles
    dfs(0)
    return total_fuel