Create 497.cpp

497.cpp

@@ -0,0 +1,99 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+// Number of vertices in the graph
+#define V 4
+
+void printSolution(int color[]);
+
+// check if the colored
+// graph is safe or not
+bool isSafe(bool graph[V][V], int color[])
+{
+	// check for every edge
+	for (int i = 0; i < V; i++)
+		for (int j = i + 1; j < V; j++)
+			if (graph[i][j] && color[j] == color[i])
+				return false;
+	return true;
+}
+
+/* This function solves the m Coloring
+problem using recursion. It returns
+false if the m colours cannot be assigned,
+otherwise, return true and prints
+assignments of colours 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, int i,
+				int color[V])
+{
+	// if current index reached end
+	if (i == V) {
+
+		// if coloring is safe
+		if (isSafe(graph, color)) {
+
+			// Print the solution
+			printSolution(color);
+			return true;
+		}
+		return false;
+	}
+
+	// Assign each color from 1 to m
+	for (int j = 1; j <= m; j++) {
+		color[i] = j;
+
+		// Recur of the rest vertices
+		if (graphColoring(graph, m, i + 1, color))
+			return true;
+
+		color[i] = 0;
+	}
+
+	return false;
+}
+
+/* A utility function to print solution */
+void printSolution(int color[])
+{
+	cout << "Solution Exists:" " Following are the assigned colors \n";
+	for (int i = 0; i < V; i++)
+		cout << " " << color[i];
+	cout << "\n";
+}
+
+// Driver code
+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
+
+	// 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;
+
+	if (!graphColoring(graph, m, 0, color))
+		cout << "Solution does not exist";
+
+	return 0;
+}
+