Question

Formatted question description: https://leetcode.ca/all/332.html

 332	Reconstruct Itinerary

 Given a list of airline tickets represented by pairs of departure and arrival airports [from, to],
 reconstruct the itinerary in order.

 All of the tickets belong to a man who departs from JFK. Thus, the itinerary must begin with JFK.

 Note:

     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"].

     All airports are represented by three capital letters (IATA code).

     You may assume all tickets form at least one valid itinerary.


 Example 1:

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


 Example 2:

 Input: [["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.

 @tag-graph

Algorithm

First of all, the graph is established, through the adjacency linked list.

Since the problem requires the solution to be small in alphabetical order, then we consider using multiset, which can be automatically sorted.

After our graph is built, we start traversal from node JFK. As long as there is a node in the multiset mapped by the current node, we take this node out, delete it in the multiset, and then continue to recursively traverse this node.

Finally, the order of our results is the opposite of what we need, we will flip it again at the end.

Code

Java

  • import java.util.*;
    
    public class Reconstruct_Itinerary {
    
        public static void main(String[] args) {
            Reconstruct_Itinerary out = new Reconstruct_Itinerary();
            Solution s = out.new Solution();
    
            System.out.println(s.findItinerary(Arrays.asList(
                Arrays.asList("JFK","SFO"),
                Arrays.asList("JFK","ATL"),
                Arrays.asList("SFO","ATL"),
                Arrays.asList("ATL","JFK"),
                Arrays.asList("ATL","SFO")
            )));
        }
    
    
        public class Solution {
            public List<String> findItinerary(List<List<String>> tickets) {
    
                List<String> result = new ArrayList<>();
    
                if (tickets == null || tickets.size() == 0) {
                    return result;
                }
    
                // step 1: build the ajdList
                // start => list of destinations
                Map<String, List<String>> adjList = new HashMap<>();
                for (List<String> ticket : tickets) {
                    String from = ticket.get(0);
                    String to = ticket.get(1);
    
                    if (adjList.containsKey(from)) {
                        adjList.get(from).add(to);
                    } else {
                        List<String> neighbors = new ArrayList<>();
                        neighbors.add(to);
                        adjList.put(from, neighbors);
                    }
                }
    
                // step 2: sort the adjlist according to lex order
                for (String from : adjList.keySet()) {
                    List<String> neighbors = adjList.get(from);
                    Collections.sort(neighbors);
                }
    
                // step 3: start the dfs
                findItineraryDfs("JFK", adjList, result);
    
                return result;
            }
    
            private void findItineraryDfs(String curr, Map<String, List<String>> adjList, List<String> result) {
    
                List<String> neighbors = adjList.get(curr);
    
                if (neighbors != null) {
                    while (neighbors.size() > 0) {
                        String neighbor = neighbors.get(0); // get first one, lex order
                        neighbors.remove(0); // @note: here is the duplicate removal part, next recursion will not have this neighbour
    
                        findItineraryDfs(neighbor, adjList, result);
                    }
                }
    
                result.add(0, curr);
            }
        }
    }
    
    public class Solution_lambda_dfs {
    
        // default heap order is min-at-top, so ensure lexical order of result
        Map<String, PriorityQueue<String>> targets = new HashMap<>();
        List<String> route = new LinkedList<>();
    
        // Java Lambda
        public List<String> findItinerary(List<List<String>> tickets) {
            Map<String, PriorityQueue<String>> targets = new HashMap<>();
            for (List<String> ticket : tickets)
                targets.computeIfAbsent(ticket.get(0), k -> new PriorityQueue<>()).add(ticket.get(1));
            dfs("JFK");
            return route;
        }
    
        void dfs(String airport) {
            while (targets.containsKey(airport) && !targets.get(airport).isEmpty())
                dfs(targets.get(airport).poll());
            route.add(0, airport);
        }
    
    }
    
    
  • // OJ: https://leetcode.com/problems/reconstruct-itinerary/
    // Time: O(E^2)
    // Space: O(E)
    class Solution {
    public:
        vector<string> findItinerary(vector<vector<string>>& E) {
            int N = E.size();
            vector<bool> used(N);
            unordered_map<string, vector<pair<string, int>>> G;
            for (int i = 0; i < E.size(); ++i) G[E[i][0]].emplace_back(E[i][1], i);
            for (auto &[u, vs] : G) sort(begin(vs), end(vs));
            vector<string> path{"JFK"};
            function<bool()> dfs = [&]() {
                if (path.size() == N + 1) return true;
                for (auto &[v, index] : G[path.back()]) {
                    if (used[index]) continue;
                    used[index] = true;
                    path.push_back(v);
                    if (dfs()) return true;
                    path.pop_back();
                    used[index] = false;
                }
                return false;
            };
            dfs();
            return path;
        }
    };
    
  • from collections import deque
    
    
    class Solution(object):
      def findItinerary(self, tickets):
        """
        :type tickets: List[List[str]]
        :rtype: List[str]
        """
        graph = {}
        hashset = set([])
        for ticket in tickets:
          graph[ticket[0]] = graph.get(ticket[0], []) + [ticket[1]]
    
        maxLen = len(tickets) + 1
    
        for k in graph:
          graph[k] = deque(sorted(graph[k]))
    
        def dfs(path, graph, maxLen, start):
          if len(path) == maxLen:
            return path + []
          for k in range(0, len(graph.get(start, []))):
            nbr = graph.get(start, [])
            top = nbr.popleft()
            path.append(top)
            ret = dfs(path, graph, maxLen, top)
            if ret:
              return ret
            path.pop()
            nbr.append(top)
          return []
    
        return dfs(["JFK"], graph, maxLen, "JFK")
    
    

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