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'

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.

Following is the implementation of the above algorithm.

## C++

`// A C++ program to order of characters in an alien language ` `#include<iostream> ` `#include <list> ` `#include <stack> ` `#include <cstring> ` `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 fidns and prints order of characer 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 'aplha' 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<Integer>[] 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<Integer> 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<Integer> 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 fidns and prints order ` ` ` `// of characer 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` `alpha) ` ` ` `{ ` ` ` `// Create a graph with 'aplha' edges ` ` ` `Graph graph = ` `new` `Graph(alpha); ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < words.length - ` `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` `); ` ` ` `} ` `} ` ` ` `//Contributed by Harikrishnan Rajan ` |

Output:

c a b

**Time Complexity: **The first step to create a graph takes O(n + alhpa) 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 + aplha) here. So overall time complexity is O(n + aplha) + O(n + aplha) which is O(n + aplha).

**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”.

This article is contributed by **Piyush Gupta**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Kahn's algorithm for Topological Sorting
- Word Ladder (Length of shortest chain to reach a target word)
- Snake and Ladder Problem
- Find if an array of strings can be chained to form a circle | Set 1
- C++ Program to print all palindromes in a given range
- Find Excel column name from a given column number
- Sorting Terminology
- Longest Path in a Directed Acyclic Graph
- Topological Sorting
- Prim’s Minimum Spanning Tree (MST) | Greedy Algo-5
- Graph and its representations
- Lexicographic rank of a string
- Floyd Warshall Algorithm | DP-16
- Detect Cycle in a Directed Graph
- Depth First Search or DFS for a Graph