Using ANSI/ISO C++, Java, or Python write a program that implements a backtracki
ID: 3820322 • Letter: U
Question
Using ANSI/ISO C++, Java, or Python write a program that implements a backtracking algorithm that solves the m-Coloring Problem as presented in class and given in your text. Your program should conform to the following specifications.
Prompt the user for the number of vertices in the graph.
Prompt the user to enter the adjacency matrix of the graph one row at a time.
Print the adjacency matrix of the graph.
Prompt the user for the maximum number of colors to be used.
Print the first solution and ask the user if they want the rest of the solutions.
If the user indicates they want the rest of the solutions, print them without any additional prompts.
Explanation / Answer
This How it goes The program to implement the back tracking algorithm.
#include<stdio.h>
// Number of vertices in the graph
#define V 4
void printSolution(int color[]);
/* A utility function to check if the current color assignment
is safe for vertex v */
bool isSafe (int v, bool graph[V][V], int color[], int c)
{
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
}
/* A recursive utility function to solve m coloring problem */
bool graphColoringUtil(bool graph[V][V], int m, int color[], int v)
{
/* base case: If all vertices are assigned a color then
return true */
if (v == V)
return true;
/* Consider this vertex v and try different colors */
for (int c = 1; c <= m; c++)
{
/* Check if assignment of color c to v is fine*/
if (isSafe(v, graph, color, c))
{
color[v] = c;
/* recur to assign colors to rest of the vertices */
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
/* If assigning color c doesn't lead to a solution
then remove it */
color[v] = 0;
}
}
/* If no color can be assigned to this vertex then return false */
return false;
}
/* This function solves the m Coloring problem using Backtracking.
It mainly uses graphColoringUtil() to solve the problem. It returns
false if the m colors cannot be assigned, otherwise return true and
prints assignments of colors to all vertices. Please note that there
may be more than one solutions, this function prints one of the
feasible solutions.*/
bool graphColoring(bool graph[V][V], int m)
{
// Initialize all color values as 0. This initialization is needed
// correct functioning of isSafe()
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
// Call graphColoringUtil() for vertex 0
if (graphColoringUtil(graph, m, color, 0) == false)
{
printf("Solution does not exist");
return false;
}
// Print the solution
printSolution(color);
return true;
}
/* A utility function to print solution */
void printSolution(int color[])
{
printf("Solution Exists:"
" Following are the assigned colors ");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf(" ");
}
// driver program to test above function
int main()
{
/* Create following graph and test whether it is 3 colorable
(3)---(2)
| / |
| / |
| / |
(0)---(1)
*/
bool graph[V][V] = {{0, 1, 1, 1},
{1, 0, 1, 0},
{1, 1, 0, 1},
{1, 0, 1, 0},
};
int m = 3; // Number of colors
graphColoring (graph, m);
return 0;
}
Output:
#include<stdio.h>
// Number of vertices in the graph
#define V 4
void printSolution(int color[]);
/* A utility function to check if the current color assignment
is safe for vertex v */
bool isSafe (int v, bool graph[V][V], int color[], int c)
{
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
}
/* A recursive utility function to solve m coloring problem */
bool graphColoringUtil(bool graph[V][V], int m, int color[], int v)
{
/* base case: If all vertices are assigned a color then
return true */
if (v == V)
return true;
/* Consider this vertex v and try different colors */
for (int c = 1; c <= m; c++)
{
/* Check if assignment of color c to v is fine*/
if (isSafe(v, graph, color, c))
{
color[v] = c;
/* recur to assign colors to rest of the vertices */
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
/* If assigning color c doesn't lead to a solution
then remove it */
color[v] = 0;
}
}
/* If no color can be assigned to this vertex then return false */
return false;
}
/* This function solves the m Coloring problem using Backtracking.
It mainly uses graphColoringUtil() to solve the problem. It returns
false if the m colors cannot be assigned, otherwise return true and
prints assignments of colors to all vertices. Please note that there
may be more than one solutions, this function prints one of the
feasible solutions.*/
bool graphColoring(bool graph[V][V], int m)
{
// Initialize all color values as 0. This initialization is needed
// correct functioning of isSafe()
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
// Call graphColoringUtil() for vertex 0
if (graphColoringUtil(graph, m, color, 0) == false)
{
printf("Solution does not exist");
return false;
}
// Print the solution
printSolution(color);
return true;
}
/* A utility function to print solution */
void printSolution(int color[])
{
printf("Solution Exists:"
" Following are the assigned colors ");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf(" ");
}
// driver program to test above function
int main()
{
/* Create following graph and test whether it is 3 colorable
(3)---(2)
| / |
| / |
| / |
(0)---(1)
*/
bool graph[V][V] = {{0, 1, 1, 1},
{1, 0, 1, 0},
{1, 1, 0, 1},
{1, 0, 1, 0},
};
int m = 3; // Number of colors
graphColoring (graph, m);
return 0;
}
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