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Problem solution · Java

Count Pairs of Connectable Servers in a Weighted Tree Network

Count Pairs of Connectable Servers in a Weighted Tree Network: a Java solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
54 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Count Pairs of Connectable Servers in a Weighted Tree Network, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 54 lines of Java from the credited upstream file 3067.java.
  • The implementation visibly relies on sequence storage.
  • 5 loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCount Pairs of Connectable Servers in a Weighted Tree Network · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int[] countPairsOfConnectableServers(int[][] edges, int signalSpeed) {    final int n = edges.length + 1;    int[] ans = new int[n];    List<Pair<Integer, Integer>>[] graph = new List[n];     for (int i = 0; i < n; i++)      graph[i] = new ArrayList<>();     for (final int[] edge : edges) {      final int u = edge[0];      final int v = edge[1];      final int w = edge[2];      graph[u].add(new Pair<>(v, w));      graph[v].add(new Pair<>(u, w));    }     for (int i = 0; i < n; ++i)      ans[i] = connectablePairsRootedAt(graph, i, signalSpeed);     return ans;  }   // Returns the number of server pairs that are connectable through the server  // `u`.  private int connectablePairsRootedAt(List<Pair<Integer, Integer>>[] graph, int u,                                       int signalSpeed) {    int pairs = 0;    int count = 0;    for (Pair<Integer, Integer> pair : graph[u]) {      final int v = pair.getKey();      final int w = pair.getValue();      final int childCount = dfs(graph, v, u, w, signalSpeed);      pairs += count * childCount;      count += childCount;    }    return pairs;  }   // Returns the number of servers that are connectable throught the server `u`  // (dist % signalSpeed == 0).  private int dfs(List<Pair<Integer, Integer>>[] graph, int u, int prev, int dist,                  int signalSpeed) {    int count = 0;    for (Pair<Integer, Integer> pair : graph[u]) {      final int v = pair.getKey();      final int w = pair.getValue();      if (v != prev)        count += dfs(graph, v, u, dist + w, signalSpeed);    }    return (dist % signalSpeed == 0 ? 1 : 0) + count;  }}

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