server_connection_problem.py

def getNumPairs(server_nodes, server_from, server_to, server_weight, signal_speed):
    # Step 1: Create an adjacency list to represent the graph
    graph = {i: [] for i in range(1, server_nodes + 1)}
    for i in range(len(server_from)):
        graph[server_from[i]].append((server_to[i], server_weight[i]))
        graph[server_to[i]].append((server_from[i], server_weight[i]))
    
    # Step 2: Implement Depth-First Search (DFS) to find all paths
    def dfs(start, end, path, distance):
        path.append(start)
        if start == end:
            return [(path[:], distance)]
        if start not in graph:
            return []
        
        paths = []
        for neighbor, weight in graph[start]:
            if neighbor not in path:
                new_paths = dfs(neighbor, end, path, distance + weight)
                paths.extend(new_paths)
        path.pop()
        return paths
    
    # Step 3: Count valid pairs for each server
    result = []
    for server in range(1, server_nodes + 1):
        valid_pairs = 0
        for target in range(1, server_nodes + 1):
            if server != target:
                paths = dfs(server, target, [], 0)
                for path, distance in paths:
                    if distance % signal_speed == 0:
                        valid_pairs += 1
                        break
        result.append(valid_pairs)
    
    return result

# Sample test case
server_nodes = 4
server_from = [1, 1, 2]
server_to = [2, 3, 4]
server_weight = [2, 5, 3]
signal_speed = 5

output = getNumPairs(server_nodes, server_from, server_to, server_weight, signal_speed)
print(output)  # Expected output: [2, 0, 2, 2]