Add september 17 challenge

2023 Daily Challenges/September 2023 Challenges/SEPT17_Shortest_path_visiting_all_nodes.cpp

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+class Solution {
+public:
+    // Class to carry three values at a time
+    class tuple
+    {
+        public:
+        int node; // on which current node we are standing
+        int mask; // mask of that node
+        int cost; // cost of path explore by this node
+        tuple(int node, int mask, int cost)
+        {
+            this -> node = node;
+            this -> mask = mask;
+            this -> cost = cost;
+        }
+    };
+
+
+    int shortestPathLength(vector<vector<int>>& graph) {
+        // total number of nodes present
+        int n = graph.size(); // extracting size of graph
+
+
+        queue<tuple> q; // queue of class tuple type
+
+         // set to take care which path we have already visited
+        set<pair<int, int>> vis;
+
+        int all = (1 << n) - 1; // if all nodes visited then
+
+        // we don't know which node will give us shortest path so intially for all nodes we will store in our queue
+        for(int i = 0; i < n; i++)
+        {
+            int maskValue = (1 << i); // 2 ^ i
+
+            tuple thisNode(i, maskValue, 1); // make a tuple for every nod
+
+            q.push(thisNode); // push tuple into our queue
+
+            vis.insert({i, maskValue}); // also update into our set
+        }
+
+        // Implementing BFS
+        while(q.empty() == false) // until queue is not empty
+        {
+            tuple curr = q.front(); // extracting front tuple
+            q.pop(); // pop from queuu
+
+            // if mask value becomes all, that means we have visited all of our nodes, so from here return cost - 1
+            if(curr.mask == all) 
+            {
+                return curr.cost - 1;
+            }
+
+            // if not, start exploring in its adjcant
+            for(auto &adj: graph[curr.node])
+            {
+                int bothVisitedMask = curr.mask; // current mask
+
+                // we are moving from one node o anthor node
+                bothVisitedMask = bothVisitedMask | (1 << adj); 
+
+                // make tuple of this path
+                tuple ThisNode(adj, bothVisitedMask, curr.cost + 1);
+
+                // if this path is not explored i.e
+                // if it is not present in our set then,
+                if(vis.find({adj, bothVisitedMask}) == vis.end())
+                {
+                    vis.insert({adj, bothVisitedMask}); // insert into set
+
+                    q.push(ThisNode); // also insert into queue
+                }
+            }
+
+        }
+
+        // return -1, but this condition will never come
+        return -1;
+    }
+};
+
+ // Time Complexity -> O(n + m), where n is the number of nodes and m is the number of edges in the graph.
+// Space Complexity -> O(n * 2^n), primarily due to the space used by the vis set.