New Commit

Author: coder-mayank22

Graph_Coloring.c

@@ -0,0 +1,153 @@
+#include <stdbool.h>
+#include <stdio.h>
+ 
+int V, m; // m is the number of colors
+
+void input(){
+    printf("Enter number of vertices in the graph: ");
+    scanf("%d", &V);
+    printf("Enter number of colors: ");
+    scanf("%d", &m);
+}
+
+void addEdge(int u, int v, bool graph[V][V]){
+    graph[u][v] = 1;
+    graph[v][u] = 1;
+}
+void printSolution(int color[]);
+ 
+/* To check if the current color assignment
+   is safe for vertex v i.e. checks
+   whether the edge exists or not
+   (i.e, graph[v][i]==1). If it exists
+   then checks whether the color to
+   be filled in the new vertex(c is
+   sent in the parameter) is already
+   used by its adjacent
+   vertices(i-->adj vertices) or
+   not (i.e, color[i]==c) */
+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 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
+   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[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 \n");
+    for (int i = 0; i < V; i++)
+        printf(" %d ", color[i]);
+    printf("\n");
+}
+ 
+// Driver code
+int main()
+{
+    /* Create following graph and test
+       whether it is 3 colorable
+      (3)---(2)
+       |   / |
+       |  /  |
+       | /   |
+      (0)---(1)
+    */
+    input();
+
+    bool graph[V][V];
+    int i, j, t;
+    for(i=0; i<V; i++){
+        for(j=0; j<V; j++){
+            graph[i][j] = 0;
+        }
+    }
+
+    for(i=0; i<V; i++){
+        for(j=0; j<V; j++){
+            printf("Enter edge between %d and %d (1->Yes and 0->No): ", i, j);
+            scanf("%d", &t);
+            if(t==1)
+                addEdge(i, j, graph);
+        }
+    }
+
+    printf("\nAdjacency Matrix:\n");
+    for(i=0; i<V; i++){
+        for(j=0; j<V; j++){
+            printf("%d ", graph[i][j]);
+        }
+        printf("\n");
+    }
+
+    // Function call
+    graphColoring(graph, m);
+    return 0;
+}