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Find Itinerary from a given list of tickets

  • Difficulty Level : Medium
  • Last Updated : 01 Jun, 2021

Given a list of tickets, find itinerary in order using the given list.

"Chennai" -> "Banglore"
"Bombay" -> "Delhi"
"Goa"    -> "Chennai"
"Delhi"  -> "Goa"

Bombay->Delhi, Delhi->Goa, Goa->Chennai, Chennai->Banglore,

It may be assumed that the input list of tickets is not cyclic and there is one ticket from every city except final destination.
One Solution is to build a graph and do Topological Sorting of the graph. Time complexity of this solution is O(n).
We can also use hashing to avoid building a graph. The idea is to first find the starting point. A starting point would never be on ‘to’ side of a ticket. Once we find the starting point, we can simply traverse the given map to print itinerary in order. Following are steps. 

1) Create a HashMap of given pair of tickets.  Let the created 
   HashMap be 'dataset'. Every entry of 'dataset' is of the form 
   "from->to" like "Chennai" -> "Banglore"

2) Find the starting point of itinerary.
     a) Create a reverse HashMap.  Let the reverse be 'reverseMap'
        Entries of 'reverseMap' are of the form "to->form". 
        Following is 'reverseMap' for above example.
        "Banglore"-> "Chennai" 
        "Delhi"   -> "Bombay" 
        "Chennai" -> "Goa"
        "Goa"     ->  "Delhi"
     b) Traverse 'dataset'.  For every key of dataset, check if it
        is there in 'reverseMap'.  If a key is not present, then we 
        found the starting point. In the above example, "Bombay" is
        starting point.

3) Start from above found starting point and traverse the 'dataset' 
   to print itinerary.

All of the above steps require O(n) time so overall time complexity is O(n).
Below is Java implementation of above idea.


// Java program to print itinerary in order
import java.util.HashMap;
import java.util.Map;
public class printItinerary
    // Driver function
    public static void main(String[] args)
        Map<String, String> dataSet = new HashMap<String, String>();
        dataSet.put("Chennai", "Banglore");
        dataSet.put("Bombay", "Delhi");
        dataSet.put("Goa", "Chennai");
        dataSet.put("Delhi", "Goa");
    // This function populates 'result' for given input 'dataset'
    private static void printResult(Map<String, String> dataSet)
        // To store reverse of given map
        Map<String, String> reverseMap = new HashMap<String, String>();
        // To fill reverse map, iterate through the given map
        for (Map.Entry<String,String> entry: dataSet.entrySet())
            reverseMap.put(entry.getValue(), entry.getKey());
        // Find the starting point of itinerary
        String start = null;
        for (Map.Entry<String,String> entry: dataSet.entrySet())
              if (!reverseMap.containsKey(entry.getKey()))
                   start = entry.getKey();
        // If we could not find a starting point, then something wrong
        // with input
        if (start == null)
           System.out.println("Invalid Input");
        // Once we have starting point, we simple need to go next, next
        // of next using given hash map
        String to = dataSet.get(start);
        while (to != null)
            System.out.print(start +  "->" + to + ", ");
            start = to;
            to = dataSet.get(to);


#include <bits/stdc++.h>
using namespace std;
void printItinerary(map<string, string> dataSet)
    // To store reverse of given map
    map<string, string> reversemap;
    map<string, string>::iterator it;
    // To fill reverse map, iterate through the given map
    for (it = dataSet.begin(); it!=dataSet.end(); it++)
        reversemap[it->second] = it->first;
    // Find the starting point of itinerary
    string start;
    for (it = dataSet.begin(); it!=dataSet.end(); it++)
        if (reversemap.find(it->first) == reversemap.end())
            start = it->first;
    // If we could not find a starting point, then something wrong with input
     if (start.empty())
        cout << "Invalid Input" << endl;
    // Once we have starting point, we simple need to go next,
    //next of next using given hash map
    it = dataSet.find(start);
    while (it != dataSet.end())
        cout << it->first << "->" << it->second << endl;
        it = dataSet.find(it->second);
int main()
    map<string, string> dataSet;
    dataSet["Chennai"] = "Banglore";
    dataSet["Bombay"] = "Delhi";
    dataSet["Goa"] = "Chennai";
    dataSet["Delhi"] = "Goa";
    return 0;
// C++ implementation is contributed by Aditya Goel


class Solution():
    #Solution class carries method for printing iterary
    def __init__(self):
    #method for printing iterary
    def printIterary(self,d):
        # First step : create a reversed mapping. Here also for storing key value pairs dictionary is used.
        reverse_d = dict()
        for i in d:
            reverse_d[d[i]] = i
        # Second step : find the starting point. Starting point will be that value which is not present in 'd' as key.
        for i in reverse_d:
            if reverse_d[i] not in reverse_d:
                starting_pt = reverse_d[i]
        #Third step : simply proceed one by one to print whole route. Assuming that there exist Starting point.
        while(starting_pt in d):
            print(starting_pt,"->",d[starting_pt],end=", ")
            starting_pt = d[starting_pt]
        #method prints here only. Does not return anything.
if __name__=="__main__":
    # Mapping using inbuilt data structure 'dictionary'
    d = dict()
    d["Chennai"] = "Banglore"
    d["Bombay"] = "Delhi"
    d["Goa"] = "Chennai"
    d["Delhi"] = "Goa"
    # call for method that would print Iteraty.
    obj = Solution()
Bombay->Delhi, Delhi->Goa, Goa->Chennai, Chennai->Banglore, 


This article is compiled by Rahul Jain. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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