Added dijkstra algorithm

Graph/dijkstra.cpp

@@ -0,0 +1,58 @@
+#include <iostream>
+#include <queue>
+#include <vector>
+#include <map>
+#include <algorithm>
+using namespace std;
+//number of nodes
+int V;
+//d stores the current shortest path from s to point i, infinity at first
+vector<int> d(V, INT_MAX), visited(V, 0);
+//adjacency list, store (node, length) connected to each vertex
+map<int, vector<pair<int, int> > > adj;
+void dij(int s){
+  //d is infinity expect for the start point
+  d[s] = 0;
+  //store min to max, pair(dist, node) store shortest unvisited node
+  priority_queue<pair<int, int>, greater<vector<int>>> Q;
+  Q.push(make_pair(0, s));
+  while(Q.size()){
+    pair<int, int> tmp = Q.top();//current shortest d unvisited node
+    Q.pop();
+    int node = tmp.second, dist = tmp.first;
+    //if d[node] has been updated since this pair, this is the version not updated
+    //depend on specicf problem
+    //and this distance stored, which is dist, will be less than the shortest route, d[node]
+    if (dist != d[node] || visited[node]) continue;
+    visited[node] = true;
+    int connect = adj[node].size();
+    for(int i = 0; i < connect; i++){//all nodes connected to it
+      int v = adj[node][i].first, l = adj[node][i].second;
+      if(d[v] > dist + l){
+        d[v] = dist + l;
+        Q.push(make_pair(d[v], v));//insert if distance improved
+      }
+    }
+  }//all vertices done
+}
+int main(){
+  // Initialize the graph
+  V = 5; // Example: 5 nodes
+  d.resize(V, INT_MAX);
+  visited.resize(V, 0);
+  // Add edges (example)
+  adj[0].push_back(make_pair(1, 10));
+  adj[0].push_back(make_pair(2, 5));
+  adj[1].push_back(make_pair(2, 2));
+  adj[1].push_back(make_pair(3, 1));
+  adj[2].push_back(make_pair(1, 3));
+  adj[2].push_back(make_pair(3, 9));
+  adj[2].push_back(make_pair(4, 2));
+  adj[3].push_back(make_pair(4, 4));
+  dij(0);
+  // Output the shortest distances
+  for(int i = 0; i < V; i++){
+    cout << "Shortest distance from 0 to " << i << " is " << d[i] << endl;
+  }
+  return 0;
+}