New Problem Solution - "Number of Restricted Paths From First to Last Node"

README.md

@@ -9,6 +9,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|1786|[Number of Restricted Paths From First to Last Node](https://leetcode.com/problems/number-of-restricted-paths-from-first-to-last-node/) | [C++](./algorithms/cpp/numberOfRestrictedPathsFromFirstToLastNode/NumberOfRestrictedPathsFromFirstToLastNode.cpp)|Medium|
 |1785|[Minimum Elements to Add to Form a Given Sum](https://leetcode.com/problems/minimum-elements-to-add-to-form-a-given-sum/) | [C++](./algorithms/cpp/minimumElementsToAddToFormAGivenSum/MinimumElementsToAddToFormAGivenSum.cpp)|Medium|
 |1784|[Check if Binary String Has at Most One Segment of Ones](https://leetcode.com/problems/check-if-binary-string-has-at-most-one-segment-of-ones/) | [C++](./algorithms/cpp/checkIfBinaryStringHasAtMostOneSegmentOfOnes/CheckIfBinaryStringHasAtMostOneSegmentOfOnes.cpp)|Easy|
 |1761|[Minimum Degree of a Connected Trio in a Graph](https://leetcode.com/problems/minimum-degree-of-a-connected-trio-in-a-graph/) | [C++](./algorithms/cpp/minimumDegreeOfAConnectedTrioInAGraph/MinimumDegreeOfAConnectedTrioInAGraph.cpp)|Hard|

algorithms/cpp/numberOfRestrictedPathsFromFirstToLastNode/NumberOfRestrictedPathsFromFirstToLastNode.cpp

@@ -0,0 +1,129 @@
+// Source : https://leetcode.com/problems/number-of-restricted-paths-from-first-to-last-node/
+// Author : Hao Chen
+// Date   : 2021-03-07
+
+/***************************************************************************************************** 
+ *
+ * There is an undirected weighted connected graph. You are given a positive integer n which denotes 
+ * that the graph has n nodes labeled from 1 to n, and an array edges where each edges[i] = [ui, vi, 
+ * weighti] denotes that there is an edge between nodes ui and vi with weight equal to weighti.
+ * 
+ * A path from node start to node end is a sequence of nodes [z0, z1, z2, ..., zk] such that z0 = 
+ * start and zk = end and there is an edge between zi and zi+1 where 0 <= i <= k-1.
+ * 
+ * The distance of a path is the sum of the weights on the edges of the path. Let 
+ * distanceToLastNode(x) denote the shortest distance of a path between node n and node x. A 
+ * restricted path is a path that also satisfies that distanceToLastNode(zi) > 
+ * distanceToLastNode(zi+1) where 0 <= i <= k-1.
+ * 
+ * Return the number of restricted paths from node 1 to node n. Since that number may be too large, 
+ * return it modulo 109 + 7.
+ * 
+ * Example 1:
+ * 
+ * Input: n = 5, edges = [[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]
+ * Output: 3
+ * Explanation: Each circle contains the node number in black and its distanceToLastNode value in 
+ * blue. The three restricted paths are:
+ * 1) 1 --> 2 --> 5
+ * 2) 1 --> 2 --> 3 --> 5
+ * 3) 1 --> 3 --> 5
+ * 
+ * Example 2:
+ * 
+ * Input: n = 7, edges = [[1,3,1],[4,1,2],[7,3,4],[2,5,3],[5,6,1],[6,7,2],[7,5,3],[2,6,4]]
+ * Output: 1
+ * Explanation: Each circle contains the node number in black and its distanceToLastNode value in 
+ * blue. The only restricted path is 1 --> 3 --> 7.
+ * 
+ * Constraints:
+ * 
+ * 	1 <= n <= 2 * 104
+ * 	n - 1 <= edges.length <= 4 * 104
+ * 	edges[i].length == 3
+ * 	1 <= ui, vi <= n
+ * 	ui != vi
+ * 	1 <= weighti <= 105
+ * 	There is at most one edge between any two nodes.
+ * 	There is at least one path between any two nodes.
+ ******************************************************************************************************/
+
+class Solution {
+    void printVector(vector<int>& v) {
+        cout << "[";
+        for (int i = 0; i< v.size() -1 ; i ++) {
+            cout << v[i] << ", ";
+        }
+        cout << v[v.size()-1] << "]" << endl;
+    }
+public:
+    int countRestrictedPaths(int n, vector<vector<int>>& edges) {
+        
+        // re-orginanize the graph map
+        vector<unordered_map<int, int>> graph(n);
+        for(auto e : edges) {
+            int x = e[0]-1;
+            int y = e[1]-1;
+            int d = e[2];
+            graph[x][y] = graph[y][x] = d; 
+        }
+        
+        
+        
+        //Dijkstra Algorithm
+        vector<int> distance(n, INT_MAX);
+        distance[n-1] = 0;
+        
+        auto cmp = [&](const int& lhs, const int& rhs) {return distance[lhs] > distance[rhs]; };
+        priority_queue<int, vector<int>, decltype(cmp)> nodes(cmp);
+        
+        nodes.push(n-1);
+        
+        while( !nodes.empty() ) {
+            int x = nodes.top(); nodes.pop();
+            for(const auto & [ y, d ] : graph[x]) {  
+                if ( distance[y] > d + distance[x] ) {
+                    distance[y] = d + distance[x];
+                    // if the node's distance is updated, 
+                    // it's neighbor  must be recaluated 
+                    nodes.push(y); 
+                }
+            }
+        }
+        
+        //printVector(distance);
+        
+
+        //Dynamic Programming for restric paths
+        vector<bool> visited(n, false);
+        vector<long> restriced_path(n, 0);
+        
+        nodes.push(n-1);
+        restriced_path[n-1] = 1;
+        visited[n-1] = true;
+        
+        while( !nodes.empty() ) {
+            int x = nodes.top(); nodes.pop();
+
+            //cout << x+1 << ":";
+            for(const auto & [ y, d ] : graph[x]) { 
+                
+                if ( distance[y] > distance[x]) {
+                    restriced_path[y] += restriced_path[x];
+                    restriced_path[y] %= 1000000007;
+                }
+                if (!visited[y]) {
+                    //cout << y+1 << ",";
+                    nodes.push(y);
+                    visited[y] = true;
+                }
+            }
+  
+            //cout<<endl;
+            //printVector(restriced_path);
+        }
+        //cout << "-------" <<endl;
+        //printVector(restriced_path);
+        return restriced_path[0];
+    }
+};