332, Reconstruct Itinerary

I Problem

You are given a list of airline tickets where tickets[i] = [fromi, toi] represent the departure and the arrival airports of one flight. Reconstruct the itinerary in order and return it.

All of the tickets belong to a man who departs from "JFK", thus, the itinerary must begin with "JFK". If there are multiple valid itineraries, you should return the itinerary that has the smallest lexical order when read as a single string.

• For example, the itinerary ["JFK", "LGA"] has a smaller lexical order than ["JFK", "LGB"].

You may assume all tickets form at least one valid itinerary. You must use all the tickets once and only once.

Example 1

Input: tickets = [["MUC", "LHR"], ["JFK", "MUC"], ["SFO", "SJC"], ["LHR", "SFO"]]
Output: ["JFK", "MUC", "LHR", "SFO", "SJC"]

Example 2

Input: tickets = [["JFK", "SFO"], ["JFK", "ATL"], ["SFO", "ATL"], ["ATL", "JFK"], ["ATL", "SFO"]]
Output: ["JFK", "ATL", "JFK", "SFO", "ATL", "SFO"]
Explanation: Another possible reconstruction is ["JFK", "SFO", "ATL", "JFK", "ATL", "SFO"] but it is larger in lexical order.

Constraints

• 1 <= tickets.length <= 300
• tickets[i].length == 2
• fromi.length == 3
• toi.length == 3
• fromi and toi consist of uppercase English letters.
• fromi != toi

Related Topics

• Depth-First Search
• Graph
• Eulerian Circuit

II Solution

Approach 1: Backtracking

pub fn find_itinerary(tickets: Vec<Vec<String>>) -> Vec<String> {
    const DFS: for<'a> fn(&'a Vec<Vec<String>>, &mut Vec<bool>, &mut Vec<&'a Vec<String>>, &mut Vec<String>) = 
        |tickets, used, path, res| {
            if !res.is_empty() {
                return;
            }

            if path.len() == tickets.len() {
                let len = path.len();
                path.iter().enumerate().for_each(|(i, p)| {
                    res.push(p[0].clone());
                    if i == len - 1 {
                        res.push(p[1].clone());
                    }
                });
                return;
            }

            for i in 0..tickets.len() {
                if used[i] {
                    continue;
                }
                if path.last().is_some_and(|last| last[1] != tickets[i][0]) {
                    continue;
                }
                if path.is_empty() && tickets[i][0] != "JFK" {
                    continue;
                }

                used[i] = true;
                path.push(&tickets[i]);

                DFS(tickets, used, path, res);

                used[i] = false;
                path.pop();
            }
    };
    tickets.sort_unstable();
    let mut used = vec![false; tickets.len()];
    let mut res = Vec::with_capacity(tickets.len());

    DFS(&tickets, &mut used, &mut vec![], &mut res);

    res
}

@FunctionalInterface
interface QuadrConsumer<A, B, C, D> {
    void accept(A a, B b, C c, D d);
}

QuadrConsumer<List<List<String>>, boolean[], List<List<String>>, List<String>> dfs1 =
        (tickets, used, path, res) -> {
            if (!res.isEmpty()) {
                return;
            }

            if (path.size() == tickets.size()) {
                for (int i = 0, size = path.size(); i < size; i++) {
                    res.add(path.get(i).get(0));
                    if (i == size - 1) {
                        res.add(path.get(i).get(1));
                    }
                }
                return;
            }

            for (int i = 0, size = tickets.size(); i < size; i++) {
                if (used[i]) {
                    continue;
                }
                if (!path.isEmpty() && path.getLast().get(1) != tickets.get(i).get(0)) {
                    continue;
                }
                if (path.isEmpty() && tickets.get(i).get(0) != "JFK") {
                    continue;
                }

                used[i] = true;
                path.addLast(tickets.get(i));

                this.dfs1.accept(tickets, used, path, res);

                used[i] = false;
                path.removeLast();
            }
        };

public List<String> findItinerary(List<List<String>> tickets) {
    tickets.sort(Comparator.comparing((List<String> t) -> t.getFirst()).thenComparing(List::getLast));
    boolean[] used = new boolean[tickets.size()];
    List<String> res = new ArrayList<>();

    this.dfs1.accept(tickets, used, new ArrayList<>(), res);

    return res;
}

Approach 2: Hierholzer Approach

pub fn find_itinerary(tickets: Vec<Vec<String>>) -> Vec<String> {
    let mut map = tickets
        .into_iter()
        .fold(HashMap::new(), |mut map, mut t| {
            let (to, from) = (t.remove(1), t.remove(0));

            match map.get_mut(&from) {
                None => {
                    map.insert(from, BinaryHeap::from([Reverse(to)]));
                }
                Some(heap) => {
                    heap.push(Reverse(to));
                }
            };

            map
        });
    const DFS: fn(String, &mut HashMap<String, BinaryHeap<Reverse<String>>>, &mut Vec<String>) =
        |curr, map, res| {
            while map.contains_key(&curr) && !map[&curr].is_empty() {
                let next = map
                    .get_mut(&curr)
                    .and_then(|heap| heap.pop())
                    .unwrap_or_default();

                DFS(next.0, map, res);
            }

            res.push(curr)
        };
    let mut res = vec![];

    DFS("JFK".to_string(), &mut map, &mut res);

    res.reverse();
    res
}

@FunctionalInterface
interface TriConsumer<A, B, C> {
    void accept(A a, B b, C c);
}

TriConsumer<String, Map<String, PriorityQueue<String>>, List<String>> dfs2 =
        (curr, map, res) -> {
            while (map.containsKey(curr) && !map.get(curr).isEmpty()) {
                String next = map.get(curr).poll();

                this.dfs2.accept(next, map, res);
            }

            res.add(curr);
        };

public List<String> findItinerary(List<List<String>> tickets) {
    Map<String, PriorityQueue<String>> map = new HashMap<>();
    for (List<String> t : tickets) {
        String from = t.getFirst();
        String to = t.getLast();

        PriorityQueue<String> minHeap = map.getOrDefault(from, new PriorityQueue<>());
        minHeap.add(to);

        map.put(from, minHeap);
    }
    List<String> res = new ArrayList<>();

    this.dfs2.accept("JFK", map, res);

    Collections.reverse(res);
    return res;
}