From 2eae8617b15b1bdb31c18b397743439796952576 Mon Sep 17 00:00:00 2001
From: rachitmanas <rachitmanas123321@gmail.com>
Date: Thu, 29 Oct 2020 01:57:31 +0530
Subject: [PATCH] Added Djikstra Algo for shortest path in C++

---
 Graph algorithm/DjikstrasAlgo.cpp | 126 ++++++++++++++++++++++++++++++
 1 file changed, 126 insertions(+)
 create mode 100644 Graph algorithm/DjikstrasAlgo.cpp

diff --git a/Graph algorithm/DjikstrasAlgo.cpp b/Graph algorithm/DjikstrasAlgo.cpp
new file mode 100644
index 0000000..a6d133d
--- /dev/null
+++ b/Graph algorithm/DjikstrasAlgo.cpp	
@@ -0,0 +1,126 @@
+//By Rachit Manas
+// Program to find Dijkstra's shortest path using 
+// priority_queue in STL 
+#include<bits/stdc++.h> 
+using namespace std; 
+# define INF 0x3f3f3f3f 
+
+// iPair ==> Integer Pair 
+typedef pair<int, int> iPair; 
+
+// This class represents a directed graph using 
+// adjacency list representation 
+class Graph 
+{ 
+	int V; // No. of vertices 
+
+	// In a weighted graph, we need to store vertex 
+	// and weight pair for every edge 
+	list< pair<int, int> > *adj; 
+
+public: 
+	Graph(int V); // Constructor 
+
+	// function to add an edge to graph 
+	void addEdge(int u, int v, int w); 
+
+	// prints shortest path from s 
+	void shortestPath(int s); 
+}; 
+
+// Allocates memory for adjacency list 
+Graph::Graph(int V) 
+{ 
+	this->V = V; 
+	adj = new list<iPair> [V]; 
+} 
+
+void Graph::addEdge(int u, int v, int w) 
+{ 
+	adj[u].push_back(make_pair(v, w)); 
+	adj[v].push_back(make_pair(u, w)); 
+} 
+
+// Prints shortest paths from src to all other vertices 
+void Graph::shortestPath(int src) 
+{ 
+	// Create a priority queue to store vertices that 
+	// are being preprocessed. This is weird syntax in C++. 
+	// Refer below link for details of this syntax 
+	// https://www.geeksforgeeks.org/implement-min-heap-using-stl/ 
+	priority_queue< iPair, vector <iPair> , greater<iPair> > pq; 
+
+	// Create a vector for distances and initialize all 
+	// distances as infinite (INF) 
+	vector<int> dist(V, INF); 
+
+	// Insert source itself in priority queue and initialize 
+	// its distance as 0. 
+	pq.push(make_pair(0, src)); 
+	dist[src] = 0; 
+
+	/* Looping till priority queue becomes empty (or all 
+	distances are not finalized) */
+	while (!pq.empty()) 
+	{ 
+		// The first vertex in pair is the minimum distance 
+		// vertex, extract it from priority queue. 
+		// vertex label is stored in second of pair (it 
+		// has to be done this way to keep the vertices 
+		// sorted distance (distance must be first item 
+		// in pair) 
+		int u = pq.top().second; 
+		pq.pop(); 
+
+		// 'i' is used to get all adjacent vertices of a vertex 
+		list< pair<int, int> >::iterator i; 
+		for (i = adj[u].begin(); i != adj[u].end(); ++i) 
+		{ 
+			// Get vertex label and weight of current adjacent 
+			// of u. 
+			int v = (*i).first; 
+			int weight = (*i).second; 
+
+			// If there is shorted path to v through u. 
+			if (dist[v] > dist[u] + weight) 
+			{ 
+				// Updating distance of v 
+				dist[v] = dist[u] + weight; 
+				pq.push(make_pair(dist[v], v)); 
+			} 
+		} 
+	} 
+
+	// Print shortest distances stored in dist[] 
+	printf("Vertex Distance from Source\n"); 
+	for (int i = 0; i < V; ++i) 
+		printf("%d \t\t %d\n", i, dist[i]); 
+} 
+
+// Driver program to test methods of graph class 
+int main() 
+{ 
+	// create the graph given in above fugure 
+	int V = 9; 
+	Graph g(V); 
+
+	// making above shown graph 
+	g.addEdge(0, 1, 4); 
+	g.addEdge(0, 7, 8); 
+	g.addEdge(1, 2, 8); 
+	g.addEdge(1, 7, 11); 
+	g.addEdge(2, 3, 7); 
+	g.addEdge(2, 8, 2); 
+	g.addEdge(2, 5, 4); 
+	g.addEdge(3, 4, 9); 
+	g.addEdge(3, 5, 14); 
+	g.addEdge(4, 5, 10); 
+	g.addEdge(5, 6, 2); 
+	g.addEdge(6, 7, 1); 
+	g.addEdge(6, 8, 6); 
+	g.addEdge(7, 8, 7); 
+
+	g.shortestPath(0); 
+
+	return 0; 
+}