This is a C++ Program to Perform Greedy Coloring.

The problem takes a graph as input and outputs colours of the each vertex after coloring the vertices greedily, such that adjacent vertices have different colours.

Vertex ‘1’ and ‘3’ can be coloured Red.

Vertex ‘2’ and ‘4’ can be coloured Yellow.

Program uses numbers instead colours for simplicity.

1. Start with a vertex and colour.

2. Give all its neighbouring colours a vertex, but before that keep a check on used colours and unused colours.

3. Only assign, unused colours to the upcoming vertex.

Here is source code of the C++ Program to Perform Greedy Coloring. The program is successfully compiled and tested under Linux platform. The program output is also shown below.

#include<bits/stdc++.h> using namespace std; int n,e,i,j; vector<vector<int> > graph; vector<int> color; bool vis[100011]; void greedyColoring() { color[0] = 0; for (i=1;i<n;i++) color[i] = -1; bool unused[n]; for (i=0;i<n;i++) unused[i]=0; for (i = 1; i < n; i++) { for (j=0;j<graph[i].size();j++) if (color[graph[i][j]] != -1) unused[color[graph[i][j]]] = true; int cr; for (cr=0;cr<n;cr++) if (unused[cr] == false) break; color[i] = cr; for (j=0;j<graph[i].size();j++) if (color[graph[i][j]] != -1) unused[color[graph[i][j]]] = false; } } int main() { int x,y; cout<<"Enter number of vertices and edges respectively:"; cin>>n>>e; cout<<"\n"; graph.resize(n); color.resize(n); memset(vis,0,sizeof(vis)); for(i=0;i<e;i++) { cout<<"\nEnter edge vertices of edge "<<i+1<<" :"; cin>>x>>y; x--; y--; graph[x].push_back(y); graph[y].push_back(x); } greedyColoring(); for(i=0;i<n;i++) { cout<<"Vertex "<<i+1<<" is coloured "<<color[i]+1<<"\n"; } }

1. User must first enter the number of vertices, N, and then number of edges, E, in the graph.

2. It should be followed by E lines, denoting A and B, if there is an edge between A and B.

3. The graph is stored as adjacency list.

4. Then, all vertices are assigned colours greedily, checking which is the best possible to be assigned at that moment.

Enter number of vertices and edges respectively:4 5 Enter edge vertices of edge 1 :1 2 Enter edge vertices of edge 2 :2 3 Enter edge vertices of edge 3 :3 4 Enter edge vertices of edge 4 :4 1 Enter edge vertices of edge 5 :2 4 Vertex 1 is coloured 0 Vertex 2 is coloured 1 Vertex 3 is coloured 0 Vertex 4 is coloured 2

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