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CountWaysMaxi.java

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+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+import java.util.PriorityQueue;
+class Main {
+
+    public static void main(String[] args) {
+
+        int n = 7;
+        List < List < Integer >> roads = new ArrayList < > () {
+            {
+                add(new ArrayList<Integer>(Arrays.asList(0, 6, 7)));
+                add(new ArrayList<Integer>(Arrays.asList(0, 1, 2)));
+                add(new ArrayList<Integer>(Arrays.asList(1, 2, 3)));
+                add(new ArrayList<Integer>(Arrays.asList(1, 3, 3)));
+                add(new ArrayList<Integer>(Arrays.asList(6, 3, 3)));
+                add(new ArrayList<Integer>(Arrays.asList(3, 5, 1)));
+                add(new ArrayList<Integer>(Arrays.asList(6, 5, 1)));
+                add(new ArrayList<Integer>(Arrays.asList(2, 5, 1)));
+                add(new ArrayList<Integer>(Arrays.asList(0, 4, 5)));
+                add(new ArrayList<Integer>(Arrays.asList(4, 6, 2)));
+
+            }
+        };
+        Solution obj = new Solution();
+        int ans = obj.countPaths(n, roads);
+
+        System.out.print(ans);
+        System.out.println();
+    }
+}
+class Pair {
+    int first;
+    int second;
+    public Pair(int first, int second) {
+        this.first = first;
+        this.second = second;
+    }
+}
+class Solution {
+
+    static int countPaths(int n, List < List < Integer >> roads) {
+
+        // Creating an adjacency list for the given graph.
+        ArrayList < ArrayList < Pair >> adj = new ArrayList < > ();
+        for (int i = 0; i < n; i++) {
+            adj.add(new ArrayList < > ());
+        }
+        int m = roads.size();
+        for (int i = 0; i < m; i++) {
+            adj.get(roads.get(i).get(0)).add(new Pair(roads.get(i).get(1), roads.get(i).get(2)));
+            adj.get(roads.get(i).get(1)).add(new Pair(roads.get(i).get(0), roads.get(i).get(2)));
+        }
+
+        // Defining a priority queue (min heap). 
+        PriorityQueue < Pair > pq = new PriorityQueue < Pair > ((x, y) -> x.first - y.first);
+
+        // Initializing the dist array and the ways array
+        // along with their first indices.
+        int[] dist = new int[n];
+        int[] ways = new int[n];
+        for (int i = 0; i < n; i++) {
+            dist[i] = Integer.MAX_VALUE;
+            ways[i] = 0;
+        }
+        dist[0] = 0;
+        ways[0] = 1;
+        pq.add(new Pair(0, 0));
+
+        // Define modulo value
+        int mod = (int)(1e9 + 7);
+
+        // Iterate through the graph with the help of priority queue
+        // just as we do in Dijkstra's Algorithm.
+        while (pq.size() != 0) {
+            int dis = pq.peek().first;
+            int node = pq.peek().second;
+            pq.remove();
+
+            for (Pair it : adj.get(node)) {
+                int adjNode = it.first;
+                int edW = it.second;
+
+                // This ‘if’ condition signifies that this is the first
+                // time we’re coming with this short distance, so we push
+                // in PQ and keep the no. of ways the same.
+                if (dis + edW < dist[adjNode]) {
+                    dist[adjNode] = dis + edW;
+                    pq.add(new Pair(dis + edW, adjNode));
+                    ways[adjNode] = ways[node];
+                } 
+
+                    // If we again encounter a node with the same short distance
+                    // as before, we simply increment the no. of ways.
+                    else if (dis + edW == dist[adjNode]) {
+                    ways[adjNode] = (ways[adjNode] + ways[node]) % mod;
+                }
+            }
+        }
+        // Finally, we return the no. of ways to reach
+        // (n-1)th node modulo 10^9+7.
+        return ways[n - 1] % mod;
+    }
+}