Topological Order (Kahn's Algorithm)

/*
 * Problem : Topological order.
 * Input   : n and m, then m rule lines.
 * Output  : The order or cycle.
 * Approach: Kahn's algorithm with a heap.
 * Time    : O((n + m) log n)
 * Space   : O(n + m)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static String solve(String[] lines) {
        String[] header = lines[0].split(" ");
        int n = Integer.parseInt(header[0]);

        // Step 1: Build the graph. indegree[v] = how many edges point to v.
        java.util.List<java.util.List<Integer>> next = new java.util.ArrayList<>();
        int[] indegree = new int[n];
        for (int i = 0; i < n; i++) {
            next.add(new java.util.ArrayList<>());
        }
        for (int i = 1; i < lines.length; i++) {
            String[] edge = lines[i].split(" ");
            int from = Integer.parseInt(edge[0]);
            int to = Integer.parseInt(edge[1]);
            next.get(from).add(to);
            indegree[to]++;
        }

        // Step 2: A PriorityQueue always gives the smallest ready node. Ready means: no unfinished edge points to it.
        java.util.PriorityQueue<Integer> ready = new java.util.PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            if (indegree[i] == 0) {
                ready.add(i);
            }
        }

        // Step 3: Take a ready node, put it in the order and remove its edges. New ready nodes join the queue.
        StringBuilder order = new StringBuilder();
        int taken = 0;
        while (!ready.isEmpty()) {
            int node = ready.poll();
            order.append(taken == 0 ? "" : " ").append(node);
            taken++;
            for (int target : next.get(node)) {
                indegree[target]--;
                if (indegree[target] == 0) {
                    ready.add(target);
                }
            }
        }

        // Step 4: If some nodes were never ready, there is a cycle and no valid order exists.
        return taken == n ? order.toString() : "cycle";
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        java.util.List<String> all = new java.util.ArrayList<>();
        while (scanner.hasNextLine()) {
            String line = scanner.nextLine().trim();
            if (!line.isEmpty()) {
                all.add(line);
            }
        }
        String[] lines = all.toArray(new String[0]);
        System.out.println(solve(lines));
    }
}