two clique problem code example

Example: Implement two clique problem

// C++ program to find out whether a given graph can be 
// converted to two Cliques or not. 
#include <bits/stdc++.h> 
using namespace std; 
  
const int V = 5; 
  
// This function returns true if subgraph reachable from 
// src is Bipartite or not. 
bool isBipartiteUtil(int G[][V], int src, int colorArr[]) 
{ 
    colorArr[src] = 1; 
  
    // Create a queue (FIFO) of vertex numbers and enqueue 
    // source vertex for BFS traversal 
    queue <int> q; 
    q.push(src); 
  
    // Run while there are vertices in queue (Similar to BFS) 
    while (!q.empty()) 
    { 
        // Dequeue a vertex from queue 
        int u = q.front(); 
        q.pop(); 
  
        // Find all non-colored adjacent vertices 
        for (int v = 0; v < V; ++v) 
        { 
            // An edge from u to v exists and destination 
            // v is not colored 
            if (G[u][v] && colorArr[v] == -1) 
            { 
                // Assign alternate color to this adjacent 
                // v of u 
                colorArr[v] = 1 - colorArr[u]; 
                q.push(v); 
            } 
  
            // An edge from u to v exists and destination 
            // v is colored with same color as u 
            else if (G[u][v] && colorArr[v] == colorArr[u]) 
                return false; 
        } 
    } 
  
    // If we reach here, then all adjacent vertices can 
    // be colored with alternate color 
    return true; 
} 
  
// Returns true if a Graph G[][] is Bipartite or not. Note 
// that G may not be connected. 
bool isBipartite(int G[][V]) 
{ 
    // Create a color array to store colors assigned 
    // to all veritces. Vertex number is used as index in 
    // this array. The value '-1' of  colorArr[i] 
    // is used to indicate that no color is assigned to 
    // vertex 'i'.  The value 1 is used to indicate first 
    // color is assigned and value 0 indicates 
    // second color is assigned. 
    int colorArr[V]; 
    for (int i = 0; i < V; ++i) 
        colorArr[i] = -1; 
  
    // One by one check all not yet colored vertices. 
    for (int i = 0; i < V; i++) 
        if (colorArr[i] == -1) 
            if (isBipartiteUtil(G, i, colorArr) == false) 
                return false; 
  
    return true; 
} 
  
// Returns true if G can be divided into 
// two Cliques, else false. 
bool canBeDividedinTwoCliques(int G[][V]) 
{ 
    // Find complement of G[][] 
    // All values are complemented except 
    // diagonal ones 
    int GC[V][V]; 
    for (int i=0; i<V; i++) 
        for (int j=0; j<V; j++) 
             GC[i][j] = (i != j)?  !G[i][j] : 0; 
  
    // Return true if complement is Bipartite 
    // else false. 
    return  isBipartite(GC); 
} 
  
// Driver program to test above function 
int main() 
{ 
    int G[][V] = {{0, 1, 1, 1, 0}, 
        {1, 0, 1, 0, 0}, 
        {1, 1, 0, 0, 0}, 
        {0, 1, 0, 0, 1}, 
        {0, 0, 0, 1, 0} 
    }; 
  
    canBeDividedinTwoCliques(G) ? cout << "Yes" : 
                                  cout << "No"; 
    return 0; 
}