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3558. Number of Ways to Assign Edge Weights I 👍

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int assignEdgeWeights(vector<vector<int>>& edges) {
    const int n = edges.size() + 1;
    vector<vector<int>> graph(n + 1);

    for (const vector<int>& edge : edges) {
      const int u = edge[0];
      const int v = edge[1];
      graph[u].push_back(v);
      graph[v].push_back(u);
    }

    queue<int> q{{1}};
    vector<bool> seen(n + 1);
    seen[1] = true;
    int step = 0;

    for (step = 0; !q.empty(); ++step)
      for (int sz = q.size(); sz > 0; --sz) {
        const int u = q.front();
        q.pop();
        for (const int v : graph[u])
          if (!seen[v]) {
            q.push(v);
            seen[v] = true;
          }
      }

    return step > 0 ? modPow(2, step - 2) : 0;
  }

 private:
  static constexpr int kMod = 1'000'000'007;

  long modPow(long x, long n) {
    if (n == 0)
      return 1;
    if (n % 2 == 1)
      return x * modPow(x % kMod, (n - 1)) % kMod;
    return modPow(x * x % kMod, (n / 2)) % kMod;
  }
};

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class Solution {
  public int assignEdgeWeights(int[][] edges) {
    final int n = edges.size() + 1;
    List<Integer>[] graph = new List[n + 1];
    Arrays.setAll(graph, i -> new ArrayList<>());

    for (int[] edge : edges) {
      final int u = edge[0];
      final int v = edge[1];
      graph[u].add(v);
      graph[v].add(u);
    }

    Queue<Integer> q = new ArrayDeque<>(List.of(1));
    boolean[] seen = new boolean[n + 1];
    seen[1] = true;

    int step = 0;
    for (step = 0; !q.isEmpty(); ++step)
      for (int sz = q.size(); sz > 0; --sz) {
        final int u = q.poll();
        for (final int v : graph[u])
          if (!seen[v]) {
            q.offer(v);
            seen[v] = true;
          }
      }

    return step > 0 ? modPow(2, step - 2) : 0;
  }

  private static final int MOD = 1_000_000_007;

  private int modPow(long x, long n) {
    if (n == 0)
      return 1;
    if (n % 2 == 1)
      return (int) (x * modPow(x % MOD, (n - 1)) % MOD);
    return modPow(x * x % MOD, (n / 2)) % MOD;
  }
}

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class Solution:
  def assignEdgeWeights(self, edges: list[list[int]]) -> int:
    MOD = 1_000_000_007
    n = len(edges) + 1
    graph = [[] for _ in range(n + 1)]

    for u, v in edges:
      graph[u].append(v)
      graph[v].append(u)

    q = collections.deque([1])
    seen = {1}

    step = 0
    while q:
      for _ in range(len(q)):
        u = q.popleft()
        for v in graph[u]:
          if v not in seen:
            q.append(v)
            seen.add(v)
      step += 1

    return pow(2, step - 2, MOD) if step > 0 else 0