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2477. Minimum Fuel Cost to Report to the Capital 👍

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  long long minimumFuelCost(vector<vector<int>>& roads, int seats) {
    long ans = 0;
    vector<vector<int>> tree(roads.size() + 1);

    for (const vector<int>& road : roads) {
      const int u = road[0];
      const int v = road[1];
      tree[u].push_back(v);
      tree[v].push_back(u);
    }

    dfs(tree, 0, -1, seats, ans);
    return ans;
  }

 private:
  int dfs(const vector<vector<int>>& tree, int u, int prev, int seats,
          long& ans) {
    int people = 1;
    for (const int v : tree[u])
      if (v != prev)
        people += dfs(tree, v, u, seats, ans);
    if (u > 0)
      // the number of cars needed = ceil(people / seats)
      ans += (people + seats - 1) / seats;
    return people;
  }
};

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class Solution {
  public long minimumFuelCost(int[][] roads, int seats) {
    List<Integer>[] tree = new List[roads.length + 1];

    for (int i = 0; i < tree.length; ++i)
      tree[i] = new ArrayList<>();

    for (int[] road : roads) {
      final int u = road[0];
      final int v = road[1];
      tree[u].add(v);
      tree[v].add(u);
    }

    dfs(tree, 0, -1, seats);
    return ans;
  }

  private long ans = 0;

  private int dfs(List<Integer>[] tree, int u, int prev, int seats) {
    int people = 1;
    for (final int v : tree[u])
      if (v != prev)
        people += dfs(tree, v, u, seats);
    if (u > 0)
      // the number of cars needed = ceil(people / seats)
      ans += (people + seats - 1) / seats;
    return people;
  }
}

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class Solution:
  def minimumFuelCost(self, roads: list[list[int]], seats: int) -> int:
    ans = 0
    tree = [[] for _ in range(len(roads) + 1)]

    for u, v in roads:
      tree[u].append(v)
      tree[v].append(u)

    def dfs(u: int, prev: int) -> int:
      nonlocal ans
      people = 1 + sum(dfs(v, u) for v in tree[u] if v != prev)
      if u > 0:
        # the number of cars needed
        ans += int(math.ceil(people / seats))
      return people

    dfs(0, -1)
    return ans