Merge pull request #581 from madihamallick/master

Added Graph Coloring Problem in C

Author: smv1999

Backtracking/graph_coloring.c

@@ -0,0 +1,83 @@
+/*Write a program to implement the graph coloring problem with  m=3 using back tracking method. Consider the  
+following adjacency matrix for the graph. 
+           1 2 3 4
+        1  0 1 1 1
+        2  1 0 1 0
+        3  1 1 0 1
+        4  1 0 1 0
+*/
+#include<stdio.h>
+#define v 4
+void printsol(int color[]) {
+	int i;
+	printf("The assigned colors are: ");
+	for (i = 0; i < v; i++)
+		printf(" %d ", color[i]);
+	printf("\n");
+}
+
+int isSafe(int adj[v][v], int color[]) {
+	int i,j;
+	for (i = 0; i < v; i++)
+		for (j = i + 1; j < v; j++)
+			if (adj[i][j] && color[j] == color[i]){
+				return 1;
+			}
+	return 0;
+}
+int graphcolor(int adj[v][v], int m, int i, int color[v]){
+	int j;
+	if (i == v){ // If we got all the vertex colored we check if it is safe
+		if (isSafe(adj, color) == 0) {
+			// If yes we print solution and return 0
+			printsol(color);
+			return 0;
+		} else{
+			return 1;
+		}
+	}
+	//Recursively colors all the vertex
+	for(j=1;j<=m;j++){
+		color[i] = j;
+		if (graphcolor(adj,m,i+1,color) == 0){ // Since we returned 0 i.e we got one solution we return the func
+			return 0;
+		}
+		color[i] = 0; // If we didn't get safe solu (i.e return value is 1) we start again
+	}
+	return 1;
+}
+
+int main(){
+	int i,j,m;
+	printf("Enter the number of colors [m] : ");
+	scanf("%d",&m);
+	int adj[v][v];
+	printf("\nEnter values of the Adjacency Matrix: \n");
+	for(i=0;i<v;i++){
+		for(j=0;j<v;j++){
+			printf("\nEnter the value of adj[%d][%d]: ",i,j);
+			scanf("%d",&adj[i][j]);
+		}
+		printf("\n");
+	}
+	printf("\n\n");
+	printf("Adjacency Matrix: \n");
+	for(i=0;i<v;i++){
+		for(j=0;j<v;j++){
+			printf("%d ",adj[i][j]);
+		}
+		printf("\n");
+	}
+	printf("\nThe value of m is: %d \nThe value of v is: %d\n",m,v);
+	
+	int color[v]; //Keeps record of the color, each vertex is colored with
+    for (i = 0; i < v; i++){
+        color[i] = 0; //first set all the nodes color as 0
+    }
+ 
+    if (graphcolor(adj, m, 0, color) == 1){
+    	printf("Solution does not exist");
+	}
+	return 0;
+}
+