# C++ Program to Demonstrate the Implementation of 4-Color Problem

C++Server Side ProgrammingProgramming

This is a C++ Program to Demonstrate the Implementation of 4-Color Problem.

## Algorithm

Begin
Develop function issafe() to check if the current color assignment
is safe for vertex v i.e. checks whether the edge exists or not.
If it exists,
then next check whether the color to be filled in the new vertex is already used by its adjacent vertices.
End
Begin
Function graphColoringtil(bool graph[V][V], int m, int col[], int v)
solve 4 coloring problem:
Here,
g[V][V] = It is a 2D array where V is the number of vertices in graph
m = maximum number of colors that can be used.
col[] = an color array that should have numbers from 1 to m.
if v == V
return true
For c = 1 to m
if (isSafe(v, g, col, c))
col[v] = c
if (graphColoringtil (g, k, col, v+1) == true)
return true
col[v] = 0
return false
End

Begin
function graphColor():
It mainly uses graphColoringUtil() to solve the problem.
It returns false if the m colors cannot be assigned,
otherwise return true.
End

## Example

#include <iostream>
#include <cstdio>
#define V 5
using namespace std;
bool isSafe (int v, bool graph[V][V], int col[], int C) {
for (int i = 0; i < V; i++)
if (graph[v][i] && C == col[i])
return false;
return true;
}
bool graphColoringtil(bool g[V][V], int k, int col[], int v) {
if (v == V) //If all vertices are assigned a color then
return true;
for (int c = 1; c <= k; c++) { //Consider this vertex v and try different colors
if (isSafe(v, g, col, c)) { //Check if assignment of color c to v is fine
col[v] = c;
if (graphColoringtil (g, k, col, v+1) == true) //recur to assign colors to rest of the vertices
return true;
col[v] = 0; //If assigning color c doesn't lead to a solution then remove it
}
}
return false;
}
void solution(int color[]) {
cout<<"The assigned colors are: \n";
for (int i = 0; i < V; i++)
cout<<color[i];
cout<<"\n";
}
bool graphColor(bool graph[V][V], int k) {
int *color = new int[V];
//initialize all colors value as 0
for (int i = 0; i < V; i++)
color[i] = 0;
if (graphColoringtil(graph, k, color, 0) == false) {
cout<<"Solution does not exist";
return false;
}
solution(color);
return true;
}
int main() {
bool g[V][V] = {
{0, 0, 1, 0,1},
{1, 1, 1, 0,0},
{1, 1, 0, 0,1},
{0, 1, 1, 0,0}
};
int k= 4;
graphColor(g, k);
return 0;
}

## Output

The assigned colors are:
1 2 3 1 1