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# Given a sorted dictionary of an alien language, find order of characters

Given a sorted dictionary (array of words) of an alien language, find order of characters in the language.

Examples:

```Input:  words[] = {"baa", "abcd", "abca", "cab", "cad"}
Output: Order of characters is 'b', 'd', 'a', 'c'
Note that words are sorted and in the given language "baa"
comes before "abcd", therefore 'b' is before 'a' in output.
Similarly we can find other orders.

Input:  words[] = {"caa", "aaa", "aab"}
Output: Order of characters is 'c', 'a', 'b'```
Recommended Practice

### Approach 1:

The idea is to create a graph of characters and then find topological sorting of the created graph. Following are the detailed steps.
1) Create a graph g with number of vertices equal to the size of alphabet in the given alien language. For example, if the alphabet size is 5, then there can be 5 characters in words. Initially there are no edges in graph.
2) Do following for every pair of adjacent words in given sorted array.
…..a) Let the current pair of words be word1 and word2. One by one compare characters of both words and find the first mismatching characters.
…..b) Create an edge in g from mismatching character of word1 to that of word2.
3) Print topological sorting of the above created graph.

The implementation of the above is in C++.

## C++

 `#include ``using` `namespace` `std;` `void` `addEdge(vector<``int``> adj[], ``char` `u, ``char` `v) {``    ``adj[u - ``'a'``].push_back(v - ``'a'``);``}` `void` `topologicalSortUtil(vector<``int``> adj[], ``int` `u, ``bool` `visited[], stack<``int``> &st) {``    ``visited[u] = ``true``;` `    ``for` `(``int` `i = 0; i < adj[u].size(); i++) {``        ``int` `v = adj[u][i];``        ``if` `(!visited[v]) {``            ``topologicalSortUtil(adj, v, visited, st);``        ``}``    ``}` `    ``st.push(u);``}` `void` `topologicalSort(vector<``int``> adj[], ``int` `V) {``    ``bool` `visited[V];``    ``stack<``int``> st;` `    ``for` `(``int` `i = 0; i < V; i++) {``        ``visited[i] = ``false``;``    ``}` `    ``for` `(``int` `i = 0; i < V; i++) {``        ``if` `(!visited[i]) {``            ``topologicalSortUtil(adj, i, visited, st);``        ``}``    ``}` `    ``while` `(!st.empty()) {``        ``cout << ``char``(st.top() + ``'a'``) << ``" "``;``        ``st.pop();``    ``}``}` `void` `printOrder(string words[], ``int` `n, ``int` `k) {``    ``vector<``int``> adj[k];` `    ``for` `(``int` `i = 0; i < n - 1; i++) {``        ``string word1 = words[i];``        ``string word2 = words[i + 1];` `        ``int` `j = 0;``        ``while` `(j < word1.length() && j < word2.length()) {``            ``if` `(word1[j] != word2[j]) {``                ``addEdge(adj, word1[j], word2[j]);``                ``break``;``            ``}``            ``j++;``        ``}``    ``}` `    ``topologicalSort(adj, k);``}` `int` `main() {``    ``string words[] = {``"baa"``, ``"abcd"``, ``"abca"``, ``"cab"``, ``"cad"``};``    ``int` `n = ``sizeof``(words) / ``sizeof``(words);``    ``int` `k = 4;` `    ``printOrder(words, n, k);` `    ``return` `0;``}`

## Java

 `import` `java.util.*;` `public` `class` `Main {``    ``public` `static` `void` `addEdge(ArrayList[] adj, ``char` `u, ``char` `v) {``        ``adj[u - ``'a'``].add(v - ``'a'``);``    ``}` `    ``public` `static` `void` `topologicalSortUtil(ArrayList[] adj, ``int` `u, ``boolean``[] visited, Stack st) {``        ``visited[u] = ``true``;` `        ``for` `(``int` `i = ``0``; i < adj[u].size(); i++) {``            ``int` `v = adj[u].get(i);``            ``if` `(!visited[v]) {``                ``topologicalSortUtil(adj, v, visited, st);``            ``}``        ``}` `        ``st.push(u);``    ``}` `    ``public` `static` `void` `topologicalSort(ArrayList[] adj, ``int` `V) {``        ``boolean``[] visited = ``new` `boolean``[V];``        ``Stack st = ``new` `Stack();` `        ``for` `(``int` `i = ``0``; i < V; i++) {``            ``visited[i] = ``false``;``        ``}` `        ``for` `(``int` `i = ``0``; i < V; i++) {``            ``if` `(!visited[i]) {``                ``topologicalSortUtil(adj, i, visited, st);``            ``}``        ``}` `        ``while` `(!st.empty()) {``            ``System.out.print((``char``) (st.pop() + ``'a'``) + ``" "``);``        ``}``    ``}` `    ``public` `static` `void` `printOrder(String[] words, ``int` `n, ``int` `k) {``        ``ArrayList[] adj = ``new` `ArrayList[k];` `        ``for` `(``int` `i = ``0``; i < k; i++) {``            ``adj[i] = ``new` `ArrayList();``        ``}` `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {``            ``String word1 = words[i];``            ``String word2 = words[i + ``1``];` `            ``int` `j = ``0``;``            ``while` `(j < word1.length() && j < word2.length()) {``                ``if` `(word1.charAt(j) != word2.charAt(j)) {``                    ``addEdge(adj, word1.charAt(j), word2.charAt(j));``                    ``break``;``                ``}``                ``j++;``            ``}``        ``}` `        ``topologicalSort(adj, k);``    ``}` `    ``public` `static` `void` `main(String[] args) {``        ``String[] words = {``"baa"``, ``"abcd"``, ``"abca"``, ``"cab"``, ``"cad"``};``        ``int` `n = words.length;``        ``int` `k = ``4``;` `        ``printOrder(words, n, k);``    ``}``}`

## Python3

 `from` `collections ``import` `defaultdict` `def` `addEdge(adj, u, v):``    ``adj[``ord``(u) ``-` `97``].append(``ord``(v) ``-` `97``)` `def` `topologicalSortUtil(adj, u, visited, st):``    ``visited[u] ``=` `True``    ` `    ``for` `v ``in` `adj[u]:``        ``if` `not` `visited[v]:``            ``topologicalSortUtil(adj, v, visited, st)``    ` `    ``st.append(u)` `def` `topologicalSort(adj, V):``    ``visited ``=` `[``False``] ``*` `V``    ``st ``=` `[]``    ` `    ``for` `i ``in` `range``(V):``        ``if` `not` `visited[i]:``            ``topologicalSortUtil(adj, i, visited, st)``    ` `    ``while` `st:``        ``print``(``chr``(st.pop() ``+` `97``), end``=``' '``)` `def` `printOrder(words, n, k):``    ``adj ``=` `defaultdict(``list``)``    ` `    ``for` `i ``in` `range``(n ``-` `1``):``        ``word1 ``=` `words[i]``        ``word2 ``=` `words[i ``+` `1``]``        ` `        ``j ``=` `0``        ``while` `j < ``len``(word1) ``and` `j < ``len``(word2):``            ``if` `word1[j] !``=` `word2[j]:``                ``addEdge(adj, word1[j], word2[j])``                ``break``            ``j ``+``=` `1``    ` `    ``topologicalSort(adj, k)` `if` `__name__ ``=``=` `'__main__'``:``    ``words ``=` `[``"baa"``, ``"abcd"``, ``"abca"``, ``"cab"``, ``"cad"``]``    ``n ``=` `len``(words)``    ``k ``=` `4``    ` `    ``printOrder(words, n, k)`

## C#

 `using` `System;``using` `System.Collections.Generic;``using` `System.Linq;` `public` `class` `MainClass``{``    ``public` `static` `void` `AddEdge(List<``int``>[] adj, ``char` `u, ``char` `v)``    ``{``        ``adj[u - ``'a'``].Add(v - ``'a'``);``    ``}` `    ``public` `static` `void` `TopologicalSortUtil(List<``int``>[] adj, ``int` `u, ``bool``[] visited, Stack<``int``> st)``    ``{``        ``visited[u] = ``true``;` `        ``foreach` `(``int` `v ``in` `adj[u])``        ``{``            ``if` `(!visited[v])``            ``{``                ``TopologicalSortUtil(adj, v, visited, st);``            ``}``        ``}` `        ``st.Push(u);``    ``}` `    ``public` `static` `void` `TopologicalSort(List<``int``>[] adj, ``int` `V)``    ``{``        ``bool``[] visited = ``new` `bool``[V];``        ``Stack<``int``> st = ``new` `Stack<``int``>();` `        ``for` `(``int` `i = 0; i < V; i++)``        ``{``            ``visited[i] = ``false``;``        ``}` `        ``for` `(``int` `i = 0; i < V; i++)``        ``{``            ``if` `(!visited[i])``            ``{``                ``TopologicalSortUtil(adj, i, visited, st);``            ``}``        ``}` `        ``while` `(st.Count > 0)``        ``{``            ``Console.Write((``char``) (st.Pop() + ``'a'``) + ``" "``);``        ``}``    ``}` `    ``public` `static` `void` `PrintOrder(``string``[] words, ``int` `n, ``int` `k)``    ``{``        ``List<``int``>[] adj = ``new` `List<``int``>[k];` `        ``for` `(``int` `i = 0; i < k; i++)``        ``{``            ``adj[i] = ``new` `List<``int``>();``        ``}` `        ``for` `(``int` `i = 0; i < n - 1; i++)``        ``{``            ``string` `word1 = words[i];``            ``string` `word2 = words[i + 1];` `            ``int` `j = 0;``            ``while` `(j < word1.Length && j < word2.Length)``            ``{``                ``if` `(word1[j] != word2[j])``                ``{``                    ``AddEdge(adj, word1[j], word2[j]);``                    ``break``;``                ``}``                ``j++;``            ``}``        ``}` `        ``TopologicalSort(adj, k);``    ``}` `    ``public` `static` `void` `Main()``    ``{``        ``string``[] words = {``"baa"``, ``"abcd"``, ``"abca"``, ``"cab"``, ``"cad"``};``        ``int` `n = words.Length;``        ``int` `k = 4;` `        ``PrintOrder(words, n, k);``    ``}``}`

## Javascript

 `function` `addEdge(adj, u, v) {``    ``adj[u.charCodeAt(0) - ``'a'``.charCodeAt(0)].push(v.charCodeAt(0) - ``'a'``.charCodeAt(0));``}` `function` `topologicalSortUtil(adj, u, visited, st) {``    ``visited[u] = ``true``;` `    ``for` `(let i = 0; i < adj[u].length; i++) {``        ``let v = adj[u][i];``        ``if` `(!visited[v]) {``            ``topologicalSortUtil(adj, v, visited, st);``        ``}``    ``}` `    ``st.push(u);``}` `function` `topologicalSort(adj, V) {``    ``let visited = ``new` `Array(V);``    ``let st = [];` `    ``for` `(let i = 0; i < V; i++) {``        ``visited[i] = ``false``;``    ``}` `    ``for` `(let i = 0; i < V; i++) {``        ``if` `(!visited[i]) {``            ``topologicalSortUtil(adj, i, visited, st);``        ``}``    ``}` `    ``while` `(st.length > 0) {``        ``process.stdout.write(String.fromCharCode(st[st.length - 1] + ``'a'``.charCodeAt(0)) + ``" "``);``        ``st.pop();``    ``}``}` `function` `printOrder(words, n, k) {``    ``let adj = ``new` `Array(k);``    ``for` `(let i = 0; i < k; i++) {``        ``adj[i] = [];``    ``}` `    ``for` `(let i = 0; i < n - 1; i++) {``        ``let word1 = words[i];``        ``let word2 = words[i + 1];` `        ``let j = 0;``        ``while` `(j < word1.length && j < word2.length) {``            ``if` `(word1[j] !== word2[j]) {``                ``addEdge(adj, word1[j], word2[j]);``                ``break``;``            ``}``            ``j++;``        ``}``    ``}` `    ``topologicalSort(adj, k);``}` `let words = [``"baa"``, ``"abcd"``, ``"abca"``, ``"cab"``, ``"cad"``];``let n = words.length;``let k = 4;` `printOrder(words, n, k);`

Output

`b d a c `

Time Complexity: The first step to create a graph takes O(n + alpha) time where n is number of given words and alpha is number of characters in given alphabet. The second step is also topological sorting. Note that there would be alpha vertices and at-most (n-1) edges in the graph. The time complexity of topological sorting is O(V+E) which is O(n + alpha) here. So overall time complexity is O(n + alpha) + O(n + alpha) which is O(n + alpha).

Space Complexity: O(V) , here V is number of Vertices.

Exercise: The above code doesn’t work when the input is not valid. For example {“aba”, “bba”, “aaa”} is not valid, because from first two words, we can deduce ‘a’ should appear before ‘b’, but from last two words, we can deduce ‘b’ should appear before ‘a’ which is not possible. Extend the above program to handle invalid inputs and generate the output as “Not valid”.

### Approach 2: [Works for invalid input data]

We have implemented this approach in C#.

#### Algorithm:

(1) Compare 2 adjacent words at a time (i.e, word1 with word2, word2 with word3, … , word(startIndex) and word(startIndex + 1)

(2) Then we compare one character at a time for the 2 words selected.

(2a) If both characters are different, we stop the comparison here and conclude that the character from word(startIndex) comes before the other.

(2b) If both characters are the same, we continue to compare until (2a) occurs or if either of the words has been exhausted.

(3) We continue to compare each word in this fashion until we have compared all words.

Once we find a character set in (2a) we pass them to class ‘AlienCharacters’ which takes care of the overall ordering of the characters. The idea is to maintain the ordering of the characters in a linked list (DNode). To optimize the insertion time into the linked list, a map (C# Dictionary) is used as an indexing entity, thus, bringing down the complexity to O(1). This is an improvement from the previous algorithm where topological sort was used for the purpose.

#### Boundary conditions:

1. The startIndex must be within range

2. When comparing 2 words, if we exhaust on one i.e, the length of both words is different. Compare only until either one exhausts.

#### Complexity Analysis:

The method-wise time complexities have been mentioned in the code below (C#) for better understanding.

If ‘N’ is the number of words in the input alien vocabulary/dictionary, ‘L’ length of the max length word, and ‘C’ is the final number of unique characters,

Time Complexity: O(N * L)
Space Complexity: O(C)

## C++

 `// A C++ program to order of characters in an alien language``#include``using` `namespace` `std;` `// Class to represent a graph``class` `Graph``{``    ``int` `V;    ``// No. of vertices'` `    ``// Pointer to an array containing adjacency listsList``    ``list<``int``> *adj;` `    ``// A function used by topologicalSort``    ``void` `topologicalSortUtil(``int` `v, ``bool` `visited[], stack<``int``> &Stack);``public``:``    ``Graph(``int` `V);   ``// Constructor` `    ``// function to add an edge to graph``    ``void` `addEdge(``int` `v, ``int` `w);` `    ``// prints a Topological Sort of the complete graph``    ``void` `topologicalSort();``};` `Graph::Graph(``int` `V)``{``    ``this``->V = V;``    ``adj = ``new` `list<``int``>[V];``}` `void` `Graph::addEdge(``int` `v, ``int` `w)``{``    ``adj[v].push_back(w); ``// Add w to v’s list.``}` `// A recursive function used by topologicalSort``void` `Graph::topologicalSortUtil(``int` `v, ``bool` `visited[], stack<``int``> &Stack)``{``    ``// Mark the current node as visited.``    ``visited[v] = ``true``;` `    ``// Recur for all the vertices adjacent to this vertex``    ``list<``int``>::iterator i;``    ``for` `(i = adj[v].begin(); i != adj[v].end(); ++i)``        ``if` `(!visited[*i])``            ``topologicalSortUtil(*i, visited, Stack);` `    ``// Push current vertex to stack which stores result``    ``Stack.push(v);``}` `// The function to do Topological Sort. It uses recursive topologicalSortUtil()``void` `Graph::topologicalSort()``{``    ``stack<``int``> Stack;` `    ``// Mark all the vertices as not visited``    ``bool` `*visited = ``new` `bool``[V];``    ``for` `(``int` `i = 0; i < V; i++)``        ``visited[i] = ``false``;` `    ``// Call the recursive helper function to store Topological Sort``    ``// starting from all vertices one by one``    ``for` `(``int` `i = 0; i < V; i++)``        ``if` `(visited[i] == ``false``)``            ``topologicalSortUtil(i, visited, Stack);` `    ``// Print contents of stack``    ``while` `(Stack.empty() == ``false``)``    ``{``        ``cout << (``char``) (``'a'` `+ Stack.top()) << ``" "``;``        ``Stack.pop();``    ``}``}` `int` `min(``int` `x, ``int` `y)``{``    ``return` `(x < y)? x : y;``}` `// This function finds and prints order of character from a sorted``// array of words. n is size of words[].  alpha is set of possible``// alphabets.``// For simplicity, this function is written in a way that only``// first 'alpha' characters can be there in words array.  For``// example if alpha is 7, then words[] should have only 'a', 'b',``// 'c' 'd', 'e', 'f', 'g'``void` `printOrder(string words[], ``int` `n, ``int` `alpha)``{``    ``// Create a graph with 'alpha' edges``    ``Graph g(alpha);` `    ``// Process all adjacent pairs of words and create a graph``    ``for` `(``int` `i = 0; i < n-1; i++)``    ``{``        ``// Take the current two words and find the first mismatching``        ``// character``        ``string word1 = words[i], word2 = words[i+1];``        ``for` `(``int` `j = 0; j < min(word1.length(), word2.length()); j++)``        ``{``            ``// If we find a mismatching character, then add an edge``            ``// from character of word1 to that of word2``            ``if` `(word1[j] != word2[j])``            ``{``                ``g.addEdge(word1[j]-``'a'``, word2[j]-``'a'``);``                ``break``;``            ``}``        ``}``    ``}` `    ``// Print topological sort of the above created graph``    ``g.topologicalSort();``}` `// Driver program to test above functions``int` `main()``{``    ``string words[] = {``"caa"``, ``"aaa"``, ``"aab"``};``    ``printOrder(words, 3, 3);``    ``return` `0;``}`

## Java

 `// A Java program to order of``// characters in an alien language``import` `java.util.*;` `// Class to represent a graph``class` `Graph {` `    ``// An array representing the graph as an adjacency list``    ``private` `final` `LinkedList[] adjacencyList;` `    ``Graph(``int` `nVertices)``    ``{``        ``adjacencyList = ``new` `LinkedList[nVertices];``        ``for` `(``int` `vertexIndex = ``0``; vertexIndex < nVertices;``             ``vertexIndex++) {``            ``adjacencyList[vertexIndex] = ``new` `LinkedList<>();``        ``}``    ``}` `    ``// function to add an edge to graph``    ``void` `addEdge(``int` `startVertex, ``int` `endVertex)``    ``{``        ``adjacencyList[startVertex].add(endVertex);``    ``}` `    ``private` `int` `getNoOfVertices()``    ``{``        ``return` `adjacencyList.length;``    ``}` `    ``// A recursive function used by topologicalSort``    ``private` `void` `topologicalSortUtil(``int` `currentVertex,``                                     ``boolean``[] visited,``                                     ``Stack stack)``    ``{``        ``// Mark the current node as visited.``        ``visited[currentVertex] = ``true``;` `        ``// Recur for all the vertices adjacent to this``        ``// vertex``        ``for` `(``int` `adjacentVertex :``             ``adjacencyList[currentVertex]) {``            ``if` `(!visited[adjacentVertex]) {``                ``topologicalSortUtil(adjacentVertex, visited,``                                    ``stack);``            ``}``        ``}` `        ``// Push current vertex to stack which stores result``        ``stack.push(currentVertex);``    ``}` `    ``// prints a Topological Sort of the complete graph``    ``void` `topologicalSort()``    ``{``        ``Stack stack = ``new` `Stack<>();` `        ``// Mark all the vertices as not visited``        ``boolean``[] visited = ``new` `boolean``[getNoOfVertices()];``        ``for` `(``int` `i = ``0``; i < getNoOfVertices(); i++) {``            ``visited[i] = ``false``;``        ``}` `        ``// Call the recursive helper function to store``        ``// Topological Sort starting from all vertices one``        ``// by one``        ``for` `(``int` `i = ``0``; i < getNoOfVertices(); i++) {``            ``if` `(!visited[i]) {``                ``topologicalSortUtil(i, visited, stack);``            ``}``        ``}` `        ``// Print contents of stack``        ``while` `(!stack.isEmpty()) {``            ``System.out.print((``char``)(``'a'` `+ stack.pop())``                             ``+ ``" "``);``        ``}``    ``}``}` `public` `class` `OrderOfCharacters {``    ``// This function finds and prints order``    ``// of character from a sorted array of words.``    ``// alpha is number of possible alphabets``    ``// starting from 'a'. For simplicity, this``    ``// function is written in a way that only``    ``// first 'alpha' characters can be there``    ``// in words array. For example if alpha``    ``//  is 7, then words[] should contain words``    ``// having only 'a', 'b','c' 'd', 'e', 'f', 'g'``    ``private` `static` `void` `printOrder(String[] words, ``int` `n,``                                   ``int` `alpha)``    ``{``        ``// Create a graph with 'alpha' edges``        ``Graph graph = ``new` `Graph(alpha);` `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {``            ``// Take the current two words and find the first``            ``// mismatching character``            ``String word1 = words[i];``            ``String word2 = words[i + ``1``];``            ``for` `(``int` `j = ``0``; j < Math.min(word1.length(),``                                         ``word2.length());``                 ``j++) {``                ``// If we find a mismatching character, then``                ``// add an edge from character of word1 to``                ``// that of word2``                ``if` `(word1.charAt(j) != word2.charAt(j)) {``                    ``graph.addEdge(word1.charAt(j) - ``'a'``,``                                  ``word2.charAt(j) - ``'a'``);``                    ``break``;``                ``}``            ``}``        ``}` `        ``// Print topological sort of the above created graph``        ``graph.topologicalSort();``    ``}` `    ``// Driver program to test above functions``    ``public` `static` `void` `main(String[] args)``    ``{``        ``String[] words = { ``"caa"``, ``"aaa"``, ``"aab"` `};``        ``printOrder(words, ``3``, ``3``);``    ``}``}` `// Contributed by Harikrishnan Rajan`

## C#

 `using` `System;``using` `System.Collections.Generic;``using` `System.Linq;` `namespace` `AlienDictionary``{``    ``public` `class` `DNode``    ``{``        ``public` `string` `Char;``        ``public` `DNode prev = ``null``;``        ``public` `DNode next = ``null``;``        ``public` `DNode(``string` `character) => Char = character;``    ``}` `    ``public` `class` `AlienCharacters``    ``{``        ``public` `AlienCharacters(``int` `k) => MaxChars = k;` `        ``private` `int` `MaxChars;``        ``private` `DNode head = ``null``;``        ``private` `Dictionary<``string``, DNode> index = ``new` `Dictionary<``string``, DNode>();``      ` `          ``// As we use Dictionary for indexing, the time complexity for inserting``        ``// characters in order will take O(1)``        ``// Time: O(1)``        ``// Space: O(c), where 'c' is the unique character count.``        ``public` `bool` `UpdateCharacterOrdering(``string` `predChar, ``string` `succChar)``        ``{``            ``DNode pNode = ``null``, sNode = ``null``;``            ``bool` `isSNodeNew = ``false``, isPNodeNew = ``false``;``            ``if``(!index.TryGetValue(predChar, ``out` `pNode))``            ``{``                ``pNode = ``new` `DNode(predChar);``                ``index[predChar] = pNode;``                ``isPNodeNew = ``true``;``            ``}``            ``if` `(!index.TryGetValue(succChar, ``out` `sNode))``            ``{``                ``sNode = ``new` `DNode(succChar);``                ``index[succChar] = sNode;``                ``isSNodeNew = ``true``;``            ``}` `            ``// before ordering is formed, validate if both the nodes are already present``            ``if` `(!isSNodeNew && !isPNodeNew)``            ``{``                ``if` `(!Validate(predChar, succChar))``                    ``return` `false``;``            ``}``            ``else` `if` `((isPNodeNew && !isSNodeNew) || (isPNodeNew && isSNodeNew))``                ``InsertNodeBefore(``ref` `pNode, ``ref` `sNode);``            ``else``                ``InsertNodeAfter(``ref` `pNode, ``ref` `sNode);` `            ``if` `(pNode.prev == ``null``)``                ``head = pNode;` `            ``return` `true``;``        ``}` `          ``// Time: O(1)``        ``private` `void` `InsertNodeAfter(``ref` `DNode pNode, ``ref` `DNode sNode)``        ``{``            ``sNode.next = pNode?.next;``            ``if` `(pNode.next != ``null``)``                ``pNode.next.prev = sNode;``            ` `            ``pNode.next = sNode;``            ``sNode.prev = pNode;``        ``}` `          ``// Time: O(1)``        ``private` `void` `InsertNodeBefore(``ref` `DNode pNode, ``ref` `DNode sNode)``        ``{``            ``// insert pnode before snode``            ``pNode.prev = sNode?.prev;` `            ``if` `(sNode.prev != ``null``)``                ``sNode.prev.next = pNode;``            ``sNode.prev = pNode;``            ``pNode.next = sNode;``        ``}` `          ``// Time: O(1)``        ``private` `bool` `Validate(``string` `predChar, ``string` `succChar)``        ``{``            ``// this is the first level of validation``            ``// validate if predChar node actually occurs before succCharNode.``            ``DNode sNode = index[succChar];` `            ``while``(sNode != ``null``)``            ``{``                ``if` `(sNode.Char != predChar)``                    ``sNode = sNode.prev;``                ``else``                    ``return` `true``; ``// validation successful``            ``}` `            ``// if we have reached the end and not found the predChar before succChar``            ``// something is not right!``            ``return` `false``;``        ``}` `          ``// Time: O(c), where 'c' is the unique character count.``        ``public` `override` `string` `ToString()``        ``{``            ``string` `res = ``""``;``            ``int` `count = 0;``            ``DNode currNode = head;` `            ``while``(currNode != ``null``)``            ``{``                ``res += currNode.Char + ``" "``;``                ``count++;``                ``currNode = currNode.next;``            ``}` `            ``// second level of validation``            ``if` `(count != MaxChars) ``// something went wrong!``                ``res = ``"ERROR!!! Input words not enough to find all k unique characters."``;` `            ``return` `res;``        ``}``    ``}` `    ``class` `Program``    ``{``        ``static` `int` `k = 4;``        ``static` `AlienCharacters alienCharacters = ``new` `AlienCharacters(k);``        ``static` `List<``string``> vocabulary = ``new` `List<``string``>();` `        ``static` `void` `Main(``string``[] args)``        ``{``            ``vocabulary.Add(``"baa"``);``            ``vocabulary.Add(``"abcd"``);``            ``vocabulary.Add(``"abca"``);``            ``vocabulary.Add(``"cab"``);``            ``vocabulary.Add(``"cad"``);` `            ``ProcessVocabulary(0);` `            ``Console.WriteLine(alienCharacters.ToString());` `            ``Console.ReadLine();``        ``}` `          ``// Time: O(vocabulary.Count + max(word.Length))``        ``static` `void` `ProcessVocabulary(``int` `startIndex)``        ``{``            ``if` `(startIndex >= vocabulary.Count - 1)``                ``return``;` `            ``var` `res = GetPredSuccChar(vocabulary.ElementAt(startIndex), vocabulary.ElementAt(startIndex + 1));``            ``if` `(res != ``null``)``            ``{``                ``if` `(!alienCharacters.UpdateCharacterOrdering(res.Item1, res.Item2))``                ``{``                    ``Console.WriteLine(``"ERROR!!! Invalid input data, the words maybe in wrong order"``);``                    ``return``;``                ``}``            ``}` `            ``ProcessVocabulary(startIndex + 1);``        ``}` `          ``//Time: O(max(str1.Length, str2.Length)``        ``static` `Tuple<``string``, ``string``> GetPredSuccChar(``string` `str1, ``string` `str2)``        ``{``            ``Tuple<``string``, ``string``> result = ``null``;` `            ``if` `(str1.Length == 0 || str2.Length == 0)``                ``return` `null``; ``// invalid condition.` `            ``if``(str1 != str2) ``// found an ordering``            ``{``                ``result = ``new` `Tuple<``string``, ``string``>(str1.ToString(), str2.ToString());``                ``return` `result;``            ``}` `            ``string` `s1 = str1.Substring(1, str1.Length - 1);``            ``string` `s2 = str2.Substring(1, str2.Length - 1);` `            ``if` `(s1.Length == 0 || s2.Length == 0)``                ``return` `null``; ``// recursion can stop now.` `            ``return` `GetPredSuccChar(s1, s2);``        ``}``    ``}``}` `// Contributed by Priyanka Pardesi Ramachander`

## Javascript

 ``

## Python3

 `# A Python program to order of characters in an alien language` `class` `Graph:``    ``def` `__init__(``self``, V):``        ``self``.V ``=` `V``        ``self``.adj ``=` `[[] ``for` `_ ``in` `range``(V)]` `    ``def` `add_edge(``self``, v, w):``        ``self``.adj[v].append(w)` `    ``def` `topological_sort_util(``self``, v, visited, stack):``        ``visited[v] ``=` `True``        ``for` `i ``in` `self``.adj[v]:``            ``if` `not` `visited[i]:``                ``self``.topological_sort_util(i, visited, stack)``        ``stack.append(v)` `    ``def` `topological_sort(``self``):``        ``stack ``=` `[]``        ``visited ``=` `[``False``] ``*` `self``.V``        ``for` `i ``in` `range``(``self``.V):``            ``if` `not` `visited[i]:``                ``self``.topological_sort_util(i, visited, stack)``        ``return` `stack` `def` `min``(x, y):``    ``return` `x ``if` `x < y ``else` `y` `def` `print_order(words, n, alpha):``    ``g ``=` `Graph(alpha)``    ``for` `i ``in` `range``(n``-``1``):``        ``word1 ``=` `words[i]``        ``word2 ``=` `words[i``+``1``]``        ``for` `j ``in` `range``(``min``(``len``(word1), ``len``(word2))):``            ``if` `word1[j] !``=` `word2[j]:``                ``g.add_edge(``ord``(word1[j])``-``ord``(``'a'``), ``ord``(word2[j])``-``ord``(``'a'``))``                ``break``    ``stack ``=` `g.topological_sort()``    ``return` `"".join([``chr``(i``+``ord``(``'a'``)) ``for` `i ``in` `stack])[::``-``1``]` `words ``=` `[``"caa"``, ``"aaa"``, ``"aab"``]``strin ``=` `print_order(words, ``len``(words), ``3``)``for` `i ``in` `strin:``      ``print``(i,end``=``' '``)` `# This code is contributed by Susobhan Akhuli`

Output:

`c a b`

Time Complexity: O(V+E) , here V is number of Vertices and E is number of Edges.

Auxiliary Space : O(V) , here V is number of Vertices.