Given an array of strings, find if the given strings can be chained to form a circle. A string X can be put before another string Y in circle if the last character of X is same as first character of Y.

Examples:

Input: arr[] = {"geek", "king"} Output: Yes, the given strings can be chained. Note that the last character of first string is same as first character of second string and vice versa is also true. Input: arr[] = {"for", "geek", "rig", "kaf"} Output: Yes, the given strings can be chained. The strings can be chained as "for", "rig", "geek" and "kaf" Input: arr[] = {"aab", "bac", "aaa", "cda"} Output: Yes, the given strings can be chained. The strings can be chained as "aaa", "aab", "bac" and "cda" Input: arr[] = {"aaa", "bbb", "baa", "aab"}; Output: Yes, the given strings can be chained. The strings can be chained as "aaa", "aab", "bbb" and "baa" Input: arr[] = {"aaa"}; Output: Yes Input: arr[] = {"aaa", "bbb"}; Output: No Input : arr[] = ["abc", "efg", "cde", "ghi", "ija"] Output : Yes These strings can be reordered as, “abc”, “cde”, “efg”, “ghi”, “ija” Input : arr[] = [“ijk”, “kji”, “abc”, “cba”] Output : No

The idea is to create a directed graph of all characters and then find if their is an eulerian circuit in the graph or not.

Graph representation of some string arrays are given in below diagram,

If there is an eulerian circuit, then chain can be formed, otherwise not.

Note that a directed graph has eulerian circuit only if in degree and out degree of every vertex is same, and all non-zero degree vertices form a single strongly connected component.

Following are detailed steps of the algorithm.

1) Create a directed graph g with number of vertices equal to the size of alphabet. We have created a graph with 26 vertices in the below program.

2) Do following for every string in the given array of strings.

…..a) Add an edge from first character to last character of the given graph.

3) If the created graph has eulerian circuit, then return true, else return false.

Following are C++ and Python implementations of the above algorithm.

## C/C++

// A C++ program to check if a given directed graph is Eulerian or not #include<iostream> #include <list> #define CHARS 26 using namespace std; // A class that represents an undirected graph class Graph { int V; // No. of vertices list<int> *adj; // A dynamic array of adjacency lists int *in; public: // Constructor and destructor Graph(int V); ~Graph() { delete [] adj; delete [] in; } // function to add an edge to graph void addEdge(int v, int w) { adj[v].push_back(w); (in[w])++; } // Method to check if this graph is Eulerian or not bool isEulerianCycle(); // Method to check if all non-zero degree vertices are connected bool isSC(); // Function to do DFS starting from v. Used in isConnected(); void DFSUtil(int v, bool visited[]); Graph getTranspose(); }; Graph::Graph(int V) { this->V = V; adj = new list<int>[V]; in = new int[V]; for (int i = 0; i < V; i++) in[i] = 0; } /* This function returns true if the directed graph has an eulerian cycle, otherwise returns false */ bool Graph::isEulerianCycle() { // Check if all non-zero degree vertices are connected if (isSC() == false) return false; // Check if in degree and out degree of every vertex is same for (int i = 0; i < V; i++) if (adj[i].size() != in[i]) return false; return true; } // A recursive function to do DFS starting from v void Graph::DFSUtil(int v, bool visited[]) { // Mark the current node as visited and print it 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]) DFSUtil(*i, visited); } // Function that returns reverse (or transpose) of this graph // This function is needed in isSC() Graph Graph::getTranspose() { Graph g(V); for (int v = 0; v < V; v++) { // Recur for all the vertices adjacent to this vertex list<int>::iterator i; for(i = adj[v].begin(); i != adj[v].end(); ++i) { g.adj[*i].push_back(v); (g.in[v])++; } } return g; } // This function returns true if all non-zero degree vertices of // graph are strongly connected. Please refer // http://www.geeksforgeeks.org/connectivity-in-a-directed-graph/ bool Graph::isSC() { // Mark all the vertices as not visited (For first DFS) bool visited[V]; for (int i = 0; i < V; i++) visited[i] = false; // Find the first vertex with non-zero degree int n; for (n = 0; n < V; n++) if (adj[n].size() > 0) break; // Do DFS traversal starting from first non zero degree vertex. DFSUtil(n, visited); // If DFS traversal doesn’t visit all vertices, then return false. for (int i = 0; i < V; i++) if (adj[i].size() > 0 && visited[i] == false) return false; // Create a reversed graph Graph gr = getTranspose(); // Mark all the vertices as not visited (For second DFS) for (int i = 0; i < V; i++) visited[i] = false; // Do DFS for reversed graph starting from first vertex. // Staring Vertex must be same starting point of first DFS gr.DFSUtil(n, visited); // If all vertices are not visited in second DFS, then // return false for (int i = 0; i < V; i++) if (adj[i].size() > 0 && visited[i] == false) return false; return true; } // This function takes an of strings and returns true // if the given array of strings can be chained to // form cycle bool canBeChained(string arr[], int n) { // Create a graph with 'aplha' edges Graph g(CHARS); // Create an edge from first character to last character // of every string for (int i = 0; i < n; i++) { string s = arr[i]; g.addEdge(s[0]-'a', s[s.length()-1]-'a'); } // The given array of strings can be chained if there // is an eulerian cycle in the created graph return g.isEulerianCycle(); } // Driver program to test above functions int main() { string arr1[] = {"for", "geek", "rig", "kaf"}; int n1 = sizeof(arr1)/sizeof(arr1[0]); canBeChained(arr1, n1)? cout << "Can be chained \n" : cout << "Can't be chained \n"; string arr2[] = {"aab", "abb"}; int n2 = sizeof(arr2)/sizeof(arr2[0]); canBeChained(arr2, n2)? cout << "Can be chained \n" : cout << "Can't be chained \n"; return 0; }

## Python

# Python program to check if a given directed graph is Eulerian or not CHARS = 26 # A class that represents an undirected graph class Graph(object): def __init__(self, V): self.V = V # No. of vertices self.adj = [[] for x in xrange(V)] # a dynamic array self.inp = [0] * V # function to add an edge to graph def addEdge(self, v, w): self.adj[v].append(w) self.inp[w]+=1 # Method to check if this graph is Eulerian or not def isSC(self): # Mark all the vertices as not visited (For first DFS) visited = [False] * self.V # Find the first vertex with non-zero degree n = 0 for n in xrange(self.V): if len(self.adj[n]) > 0: break # Do DFS traversal starting from first non zero degree vertex. self.DFSUtil(n, visited) # If DFS traversal doesn't visit all vertices, then return false. for i in xrange(self.V): if len(self.adj[i]) > 0 and visited[i] == False: return False # Create a reversed graph gr = self.getTranspose() # Mark all the vertices as not visited (For second DFS) for i in xrange(self.V): visited[i] = False # Do DFS for reversed graph starting from first vertex. # Staring Vertex must be same starting point of first DFS gr.DFSUtil(n, visited) # If all vertices are not visited in second DFS, then # return false for i in xrange(self.V): if len(self.adj[i]) > 0 and visited[i] == False: return False return True # This function returns true if the directed graph has an eulerian # cycle, otherwise returns false def isEulerianCycle(self): # Check if all non-zero degree vertices are connected if self.isSC() == False: return False # Check if in degree and out degree of every vertex is same for i in xrange(self.V): if len(self.adj[i]) != self.inp[i]: return False return True # A recursive function to do DFS starting from v def DFSUtil(self, v, visited): # Mark the current node as visited and print it visited[v] = True # Recur for all the vertices adjacent to this vertex for i in xrange(len(self.adj[v])): if not visited[self.adj[v][i]]: self.DFSUtil(self.adj[v][i], visited) # Function that returns reverse (or transpose) of this graph # This function is needed in isSC() def getTranspose(self): g = Graph(self.V) for v in xrange(self.V): # Recur for all the vertices adjacent to this vertex for i in xrange(len(self.adj[v])): g.adj[self.adj[v][i]].append(v) g.inp[v]+=1 return g # This function takes an of strings and returns true # if the given array of strings can be chained to # form cycle def canBeChained(arr, n): # Create a graph with 'aplha' edges g = Graph(CHARS) # Create an edge from first character to last character # of every string for i in xrange(n): s = arr[i] g.addEdge(ord(s[0])-ord('a'), ord(s[len(s)-1])-ord('a')) # The given array of strings can be chained if there # is an eulerian cycle in the created graph return g.isEulerianCycle() # Driver program arr1 = ["for", "geek", "rig", "kaf"] n1 = len(arr1) if canBeChained(arr1, n1): print "Can be chained" else: print "Cant be chained" arr2 = ["aab", "abb"] n2 = len(arr2) if canBeChained(arr2, n2): print "Can be chained" else: print "Can't be chained" # This code is contributed by BHAVYA JAIN

Output:

Can be chained Can't be chained

Find if an array of strings can be chained to form a circle | Set 2

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