From 9b8bfa0214bf8dd42b5d5c2be7cc9befa44527b1 Mon Sep 17 00:00:00 2001
From: VISHAL BHARTI <42848830+knightvishal@users.noreply.github.com>
Date: Fri, 15 Oct 2021 13:53:16 +0530
Subject: [PATCH] =?UTF-8?q?Create=20Dijkstra=E2=80=99s=20Shortest=20path?=
 =?UTF-8?q?=20Algorithm?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 ...stra\342\200\231s Shortest path Algorithm" | 94 +++++++++++++++++++
 1 file changed, 94 insertions(+)
 create mode 100644 "Dijkstra\342\200\231s Shortest path Algorithm"

diff --git "a/Dijkstra\342\200\231s Shortest path Algorithm" "b/Dijkstra\342\200\231s Shortest path Algorithm"
new file mode 100644
index 0000000..9432e31
--- /dev/null
+++ "b/Dijkstra\342\200\231s Shortest path Algorithm"	
@@ -0,0 +1,94 @@
+// A C++ program for Dijkstra's single source shortest path algorithm.
+// The program is for adjacency matrix representation of the graph
+#include <iostream>
+using namespace std;
+#include <limits.h>
+
+// Number of vertices in the graph
+#define V 9
+
+// A utility function to find the vertex with minimum distance value, from
+// the set of vertices not yet included in shortest path tree
+int minDistance(int dist[], bool sptSet[])
+{
+
+	// Initialize min value
+	int min = INT_MAX, min_index;
+
+	for (int v = 0; v < V; v++)
+		if (sptSet[v] == false && dist[v] <= min)
+			min = dist[v], min_index = v;
+
+	return min_index;
+}
+
+// A utility function to print the constructed distance array
+void printSolution(int dist[])
+{
+	cout <<"Vertex \t Distance from Source" << endl;
+	for (int i = 0; i < V; i++)
+		cout << i << " \t\t"<<dist[i]<< endl;
+}
+
+// Function that implements Dijkstra's single source shortest path algorithm
+// for a graph represented using adjacency matrix representation
+void dijkstra(int graph[V][V], int src)
+{
+	int dist[V]; // The output array. dist[i] will hold the shortest
+	// distance from src to i
+
+	bool sptSet[V]; // sptSet[i] will be true if vertex i is included in shortest
+	// path tree or shortest distance from src to i is finalized
+
+	// Initialize all distances as INFINITE and stpSet[] as false
+	for (int i = 0; i < V; i++)
+		dist[i] = INT_MAX, sptSet[i] = false;
+
+	// Distance of source vertex from itself is always 0
+	dist[src] = 0;
+
+	// Find shortest path for all vertices
+	for (int count = 0; count < V - 1; count++) {
+		// Pick the minimum distance vertex from the set of vertices not
+		// yet processed. u is always equal to src in the first iteration.
+		int u = minDistance(dist, sptSet);
+
+		// Mark the picked vertex as processed
+		sptSet[u] = true;
+
+		// Update dist value of the adjacent vertices of the picked vertex.
+		for (int v = 0; v < V; v++)
+
+			// Update dist[v] only if is not in sptSet, there is an edge from
+			// u to v, and total weight of path from src to v through u is
+			// smaller than current value of dist[v]
+			if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX
+				&& dist[u] + graph[u][v] < dist[v])
+				dist[v] = dist[u] + graph[u][v];
+	}
+
+	// print the constructed distance array
+	printSolution(dist);
+}
+
+// driver program to test above function
+int main()
+{
+
+	/* Let us create the example graph discussed above */
+	int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
+						{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
+						{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
+						{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
+						{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
+						{ 0, 0, 4, 14, 10, 0, 2, 0, 0 },
+						{ 0, 0, 0, 0, 0, 2, 0, 1, 6 },
+						{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
+						{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } };
+
+	dijkstra(graph, 0);
+
+	return 0;
+}
+
+// This code is contributed by shivanisinghss2110