Create Floyd Warshall Algorithm

 Solves the all-pairs shortest path problem using Floyd Warshall algorithm

Author: prasantraj0808

Pattern_Matching/src/Floyd Warshall Algorithm

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+// C++ Program for Floyd Warshall Algorithm
+#include <bits/stdc++.h>
+using namespace std;
+
+// Number of vertices in the graph
+#define V 4
+
+/* Define Infinite as a large enough
+value.This value will be used for
+vertices not connected to each other */
+#define INF 99999
+
+// A function to print the solution matrix
+void printSolution(int dist[][V]);
+
+// Solves the all-pairs shortest path
+// problem using Floyd Warshall algorithm
+void floydWarshall(int graph[][V])
+{
+	/* dist[][] will be the output matrix
+	that will finally have the shortest
+	distances between every pair of vertices */
+	int dist[V][V], i, j, k;
+
+	/* Initialize the solution matrix same
+	as input graph matrix. Or we can say
+	the initial values of shortest distances
+	are based on shortest paths considering
+	no intermediate vertex. */
+	for (i = 0; i < V; i++)
+		for (j = 0; j < V; j++)
+			dist[i][j] = graph[i][j];
+
+	/* Add all vertices one by one to
+	the set of intermediate vertices.
+	---> Before start of an iteration,
+	we have shortest distances between all
+	pairs of vertices such that the
+	shortest distances consider only the
+	vertices in set {0, 1, 2, .. k-1} as
+	intermediate vertices.
+	----> After the end of an iteration,
+	vertex no. k is added to the set of
+	intermediate vertices and the set becomes {0, 1, 2, ..
+	k} */
+	for (k = 0; k < V; k++) {
+		// Pick all vertices as source one by one
+		for (i = 0; i < V; i++) {
+			// Pick all vertices as destination for the
+			// above picked source
+			for (j = 0; j < V; j++) {
+				// If vertex k is on the shortest path from
+				// i to j, then update the value of
+				// dist[i][j]
+				if (dist[i][j] > (dist[i][k] + dist[k][j])
+					&& (dist[k][j] != INF
+						&& dist[i][k] != INF))
+					dist[i][j] = dist[i][k] + dist[k][j];
+			}
+		}
+	}
+
+	// Print the shortest distance matrix
+	printSolution(dist);
+}
+
+/* A utility function to print solution */
+void printSolution(int dist[][V])
+{
+	cout << "The following matrix shows the shortest "
+			"distances"
+			" between every pair of vertices \n";
+	for (int i = 0; i < V; i++) {
+		for (int j = 0; j < V; j++) {
+			if (dist[i][j] == INF)
+				cout << "INF"
+					<< "	 ";
+			else
+				cout << dist[i][j] << "	 ";
+		}
+		cout << endl;
+	}
+}
+
+// Driver's code
+int main()
+{
+	/* Let us create the following weighted graph
+			10
+	(0)------->(3)
+		|	 /|\
+	5 |	 |
+		|	 | 1
+	\|/	 |
+	(1)------->(2)
+			3	 */
+	int graph[V][V] = { { 0, 5, INF, 10 },
+						{ INF, 0, 3, INF },
+						{ INF, INF, 0, 1 },
+						{ INF, INF, INF, 0 } };
+
+	// Function call
+	floydWarshall(graph);
+	return 0;
+}
+
+