Find Itinerary from a given list of tickets

Last Updated : 18 Feb, 2025

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

Note: It may be assumed that the input list of tickets is not cyclic and there is one ticket from every city except the final destination.

Examples:

Input: "Chennai" -> "Bangalore"
"Bombay" -> "Delhi"
"Goa" -> "Chennai"
"Delhi" -> "Goa"
Output: Bombay->Delhi, Delhi->Goa, Goa->Chennai, Chennai->Bangalore
Input: "New York" -> "Chicago"
"Denver" -> "San Francisco"
"Chicago" -> "Denver"
"San Francisco" -> "Los Angeles"
Output: New York -> Chicago, Chicago -> Denver, Denver -> San Francisco, San Francisco -> Los Angeles

Table of Content

[Expected Approach - 1] - Using Topological Sorting - O(n) Time and O(n) Space
[Expected Approach - 2] - Using HashMap - O(n) Time and O(n) Space

[Expected Approach - 1] - Using Topological Sorting - O(n) Time and O(n) Space

The idea is to use Topological Sorting to sort the cities (nodes). Firstly, store the tickets in a HashMap to create a adjacency list, and create another HashMap to store the visited node. Also, to keep the order of cities, create a stack. Now start from any of the unvisited node and keep pushing the nodes one by one in the stack. At last push all the elements of stack in an array.

C++

#include <bits/stdc++.h>
using namespace std;

// Function to perform DFS and topological sorting
void topologicalSortUtil(string v, unordered_map<string, string> &mp, unordered_map<string, int> &visited, stack<string> &st) {
    // Mark the current node as visited
    visited[v] = 1;

    // Recur for adjacent vertex
    if (mp.find(v) != mp.end() && visited[mp[v]] == 0)
        topologicalSortUtil(mp[v], mp, visited, st);

    // Push current vertex onto stack
    if (!v.empty())
        st.push(v);
}

// Function to perform topological sort
vector<string> topologicalSort(unordered_map<string, string> &mp) {
    stack<string> st;
    unordered_map<string, int> visited;

    // Perform DFS for all vertices
    for (auto &i : mp) {
        if (visited[i.first] == 0)
            topologicalSortUtil(i.first, mp, visited, st);
    }

    vector<string> ans;
    while (!st.empty()) {
        ans.push_back(st.top());
        st.pop();
    }

    return ans;
}

// Function to find the itinerary order
vector<vector<string>> findItinerary(vector<vector<string>> &arr) {
    unordered_map<string, string> mp;

    // Map the list of tickets
    for (auto &i : arr) {
        mp[i[0]] = i[1];
    }

    vector<string> res = topologicalSort(mp);
    vector<vector<string>> ans;

    // Create itinerary pairs
    for (size_t i = 0; i < res.size() - 1; i++) {
        ans.push_back({res[i], res[i + 1]});
    }

    return ans;
}

int main() {
    vector<vector<string>> arr = {
        {"Chennai", "Bangalore"},
        {"Bombay", "Delhi"},
        {"Goa", "Chennai"},
        {"Delhi", "Goa"}
    };

    vector<vector<string>> res = findItinerary(arr);
    
    for (auto &i : res) {
        cout << i[0] << " -> " << i[1] << endl;
    }

    return 0;
}

Java

import java.util.*;

class GFG {
    
    // Function to perform DFS and topological sorting
    static void topologicalSortUtil(String v, Map<String, String> mp, Map<String, Integer> visited, Stack<String> st) {

        // mark current node as visited
        visited.put(v, 1);

        // recur for adjacent vertex
        if (mp.containsKey(v) && visited.getOrDefault(mp.get(v), 0) == 0)
            topologicalSortUtil(mp.get(v), mp, visited, st);

        // push current vertex in stack
        if (!v.isEmpty())
            st.push(v);
    }

    // Function to perform topological sort
    static List<String> topologicalSort(Map<String, String> mp) {
        int V = mp.size();

        // stack to store the result
        Stack<String> st = new Stack<>();
        Map<String, Integer> visited = new HashMap<>();

        // Call the recursive helper function to store
        // Topological Sort starting from all vertices
        for (String i : mp.keySet()) {
            if (visited.getOrDefault(i, 0) == 0)
                topologicalSortUtil(i, mp, visited, st);
        }

        List<String> ans = new ArrayList<>();
        
        // append contents of stack
        while (!st.isEmpty()) {
            ans.add(st.pop());
        }

        return ans;
    }

    static List<List<String>> findItinerary(List<List<String>> arr) {

        // map the list of tickets
        Map<String, String> mp = new HashMap<>();
        for (List<String> i : arr) {
            mp.put(i.get(0), i.get(1));
        }

        List<String> res = topologicalSort(mp);

        List<List<String>> ans = new ArrayList<>();
        for (int i = 0; i < res.size() - 1; i++) {
            ans.add(Arrays.asList(res.get(i), res.get(i + 1)));
        }
        return ans;
    }

    public static void main(String[] args) {
        List<List<String>> arr = Arrays.asList(
            Arrays.asList("Chennai", "Bangalore"),
            Arrays.asList("Bombay", "Delhi"),
            Arrays.asList("Goa", "Chennai"),
            Arrays.asList("Delhi", "Goa")
        );

        List<List<String>> res = findItinerary(arr);
        for (List<String> i : res) {
            System.out.println(i.get(0) + " -> " + i.get(1));
        }
    }
}

Python

# Function to perform DFS and topological sorting
def topologicalSortUtil(v, mp, visited, st):
    # mark current node as visited
    visited[v] = 1

    # recur for adjacent vertex
    if v in mp and visited.get(mp[v], 0) == 0:
        topologicalSortUtil(mp[v], mp, visited, st)

    # push current vertex in stack
    if v:
        st.append(v)

# Function to perform topological sort
def topologicalSort(mp):
    V = len(mp)

    # stack to store the result
    st = []
    visited = {}

    # Call the recursive helper function to store
    # Topological Sort starting from all vertices
    for i in mp:
        if visited.get(i, 0) == 0:
            topologicalSortUtil(i, mp, visited, st)

    return st[::-1]

def findItinerary(arr):
    # map the list of tickets
    mp = {i[0]: i[1] for i in arr}

    res = topologicalSort(mp)

    ans = []
    for i in range(len(res) - 1):
        ans.append([res[i], res[i + 1]])
    return ans

if __name__ == "__main__":
    arr = [
        ["Chennai", "Bangalore"],
        ["Bombay", "Delhi"],
        ["Goa", "Chennai"],
        ["Delhi", "Goa"]
    ]

    res = findItinerary(arr)
    for i in res:
        print(i[0] + " -> " + i[1])

using System;
using System.Collections.Generic;

class GFG {

    // Function to perform DFS and topological sorting
    static void topologicalSortUtil(string v, Dictionary<string, string> mp, Dictionary<string, int> visited, Stack<string> st) {

        // mark current node as visited
        visited[v] = 1;

        // recur for adjacent vertex
        if (mp.ContainsKey(v) && visited.GetValueOrDefault(mp[v], 0) == 0)
            topologicalSortUtil(mp[v], mp, visited, st);

        // push current vertex in stack
        if (!string.IsNullOrEmpty(v))
            st.Push(v);
    }

    // Function to perform topological sort
    static List<string> topologicalSort(Dictionary<string, string> mp) {

        int V = mp.Count;

        // stack to store the result
        Stack<string> st = new Stack<string>();
        Dictionary<string, int> visited = new Dictionary<string, int>();

        // Call the recursive helper function to store
        // Topological Sort starting from all vertices
        foreach (var i in mp) {
            if (!visited.ContainsKey(i.Key))
                topologicalSortUtil(i.Key, mp, visited, st);
        }

        List<string> ans = new List<string>();

        // append contents of stack
        while (st.Count > 0) {
            ans.Add(st.Pop());
        }

        return ans;
    }

    static List<List<string>> findItinerary(List<List<string>> arr) {

        // map the list of tickets
        Dictionary<string, string> mp = new Dictionary<string, string>();
        foreach (var i in arr) {
            mp[i[0]] = i[1];
        }

        List<string> res = topologicalSort(mp);

        List<List<string>> ans = new List<List<string>>();
        for (int i = 0; i < res.Count - 1; i++) {
            ans.Add(new List<string> { res[i], res[i + 1] });
        }
        return ans;
    }

    static void Main() {
        List<List<string>> arr = new List<List<string>> {
            new List<string> { "Chennai", "Bangalore" },
            new List<string> { "Bombay", "Delhi" },
            new List<string> { "Goa", "Chennai" },
            new List<string> { "Delhi", "Goa" }
        };

        List<List<string>> res = findItinerary(arr);
        foreach (var i in res) {
            Console.WriteLine(i[0] + " -> " + i[1]);
        }
    }
}

JavaScript

// Function to perform DFS and topological sorting
function topologicalSortUtil(v, mp, visited, st) {

    // mark current node as visited
    visited[v] = 1;

    // recur for adjacent vertex
    if (mp[v] && !visited[mp[v]]) 
        topologicalSortUtil(mp[v], mp, visited, st);

    // push current vertex in stack
    if (v)
        st.push(v);
}

// Function to perform topological sort
function topologicalSort(mp) {

    let V = Object.keys(mp).length;

    // stack to store the result
    let st = [];
    let visited = {};

    // Call the recursive helper function to store
    // Topological Sort starting from all vertices
    for (let i in mp) {
        if (!visited[i])
            topologicalSortUtil(i, mp, visited, st);
    }

    return st.reverse();
}

function findItinerary(arr) {

    // map the list of tickets
    let mp = {};
    arr.forEach(i => mp[i[0]] = i[1]);

    let res = topologicalSort(mp);

    let ans = [];
    for (let i = 0; i < res.length - 1; i++) {
        ans.push([res[i], res[i + 1]]);
    }
    return ans;
}

function main() {
    let arr = [
        ["Chennai", "Bangalore"],
        ["Bombay", "Delhi"],
        ["Goa", "Chennai"],
        ["Delhi", "Goa"]
    ];

    let res = findItinerary(arr);
    res.forEach(i => console.log(i[0] + " -> " + i[1]));
}

main();

Output

Bombay -> Delhi
Delhi -> Goa
Goa -> Chennai
Chennai -> Bangalore

[Expected Approach - 2] - Using HashMap - O(n) Time and O(n) Space

The idea is to store the list of tickets in a Hashmap and find the starting point of the itinerary.
To do so, firstly create a HashMap of given tickets, and also create a reverse HashMap to store the order in reverse
Now traverse the first HashMap, and search if key is present in reverse one, the node which is not present is a start point.
Now from start point traverse through all other connected nodes.

C++

#include <bits/stdc++.h>
using namespace std;

vector<vector<string>> findItinerary( 
            vector<vector<string>> &arr) {

    map<string, string> dataSet;
    for(auto i:arr) {
        dataSet[i[0]] = i[1];
    }

    map<string, string> reverseMap;
    for(auto i:arr) {
        reverseMap[i[1]] = i[0];
    }

    // Find the starting point of itinerary
    string start;

    for(int i = 0; i<arr.size(); i++) {
        if(reverseMap.count(arr[i][0]) == 0) {
            start = arr[i][0];
            break;
        }
    }

    vector<vector<string>> ans;

    // Once we have starting point, we simple need to go next,
    // next of next using given hash ma
    auto it = dataSet.find(start);
    while (it != dataSet.end()) {
        ans.push_back({it->first, it->second});
        it = dataSet.find(it->second);
    }
    
    return ans;
}

int main() {
    vector<vector<string>> arr = 
    {{"Chennai" ,"Bangalore"}, {"Bombay", "Delhi"}, 
    {"Goa", "Chennai"}, {"Delhi", "Goa"}};

    vector<vector<string>> res = findItinerary(arr);
    for(auto i:res) {
        cout<<i[0]<<" -> "<<i[1]<<endl;
    }

    return 0;
}

Java

import java.util.*;

class GFG {

    static List<List<String>> findItinerary(
                            List<List<String>> arr) {

        Map<String, String> dataSet = new HashMap<>();
        for (List<String> i : arr) {
            dataSet.put(i.get(0), i.get(1));
        }

        Map<String, String> reverseMap = new HashMap<>();
        for (List<String> i : arr) {
            reverseMap.put(i.get(1), i.get(0));
        }

        // Find the starting point of itinerary
        String start = "";

        for (int i = 0; i < arr.size(); i++) {
            if (!reverseMap.containsKey(arr.get(i).get(0))) {
                start = arr.get(i).get(0);
                break;
            }
        }

        List<List<String>> ans = new ArrayList<>();

        // Once we have starting point, we simple need to go next,
        // next of next using given hash map
        String current = start;
        while (dataSet.containsKey(current)) {
            List<String> temp = new ArrayList<>();
            temp.add(current);
            temp.add(dataSet.get(current));
            ans.add(temp);
            current = dataSet.get(current);
        }

        return ans;
    }

    public static void main(String[] args) {
        List<List<String>> arr = Arrays.asList(
                Arrays.asList("Chennai", "Bangalore"),
                Arrays.asList("Bombay", "Delhi"),
                Arrays.asList("Goa", "Chennai"),
                Arrays.asList("Delhi", "Goa")
        );

        List<List<String>> res = findItinerary(arr);
        for (List<String> i : res) {
            System.out.println(i.get(0) + " -> " + i.get(1));
        }
    }
}

Python

def findItinerary(arr):
    
    dataSet = {}
    for i in arr:
        dataSet[i[0]] = i[1]

    reverseMap = {}
    for i in arr:
        reverseMap[i[1]] = i[0]

    # Find the starting point of itinerary
    start = ""

    for i in range(len(arr)):
        if arr[i][0] not in reverseMap:
            start = arr[i][0]
            break

    ans = []

    # Once we have starting point, we simple need to go next,
    # next of next using given hash map
    while start in dataSet:
        ans.append([start, dataSet[start]])
        start = dataSet[start]

    return ans


if __name__ == "__main__":
    arr = [["Chennai", "Bangalore"], ["Bombay", "Delhi"], 
           ["Goa", "Chennai"], ["Delhi", "Goa"]]

    res = findItinerary(arr)
    for i in res:
        print(i[0], "->", i[1])

using System;
using System.Collections.Generic;

class GFG {
    
    static List<List<string>> findItinerary(
                        List<List<string>> arr) {
        
        Dictionary<string, string> dataSet = 
                new Dictionary<string, string>();
        foreach (var i in arr) {
            dataSet[i[0]] = i[1];
        }

        Dictionary<string, string> reverseMap = 
                new Dictionary<string, string>();
        foreach (var i in arr) {
            reverseMap[i[1]] = i[0];
        }

        // Find the starting point of itinerary
        string start = "";

        for (int i = 0; i < arr.Count; i++) {
            if (!reverseMap.ContainsKey(arr[i][0])) {
                start = arr[i][0];
                break;
            }
        }

        List<List<string>> ans = new List<List<string>>();

        // Once we have starting point, we simple need to go next,
        // next of next using given hash map
        while (dataSet.ContainsKey(start)) {
            ans.Add(new List<string> { start, dataSet[start] });
            start = dataSet[start];
        }

        return ans;
    }

    static void Main(string[] args) {
        List<List<string>> arr = new List<List<string>> {
            new List<string> { "Chennai", "Bangalore" },
            new List<string> { "Bombay", "Delhi" },
            new List<string> { "Goa", "Chennai" },
            new List<string> { "Delhi", "Goa" }
        };

        List<List<string>> res = findItinerary(arr);
        foreach (var i in res) {
            Console.WriteLine(i[0] + " -> " + i[1]);
        }
    }
}

JavaScript

function findItinerary(arr) {

    let dataSet = new Map();
    for (let i of arr) {
        dataSet.set(i[0], i[1]);
    }

    let reverseMap = new Map();
    for (let i of arr) {
        reverseMap.set(i[1], i[0]);
    }

    // Find the starting point of itinerary
    let start = "";

    for (let i = 0; i < arr.length; i++) {
        if (!reverseMap.has(arr[i][0])) {
            start = arr[i][0];
            break;
        }
    }

    let ans = [];

    // Once we have starting point, we simple need to go next,
    // next of next using given hash map
    while (dataSet.has(start)) {
        ans.push([start, dataSet.get(start)]);
        start = dataSet.get(start);
    }

    return ans;
}

let arr = [["Chennai", "Bangalore"], ["Bombay", "Delhi"], 
           ["Goa", "Chennai"], ["Delhi", "Goa"]];

let res = findItinerary(arr);
for (let i of res) {
    console.log(i[0] + " -> " + i[1]);
}

Output

Bombay -> Delhi
Delhi -> Goa
Goa -> Chennai
Chennai -> Bangalore

Find number of Employees Under every Manager

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Article Tags :

Practice Tags :

Hash

Find Itinerary from a given list of tickets

[Expected Approach - 1] - Using Topological Sorting - O(n) Time and O(n) Space

[Expected Approach - 2] - Using HashMap - O(n) Time and O(n) Space

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