Number of Restricted Paths from First to Last Node problem solved

Author: hasibulislam999

Shortest Path/1786_number-of-restricted-paths-from-first-to-last-node.js

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+/**
+ * Title: Number of Restricted Paths from First to Last Node
+ * Description: 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.
+ * Author: Hasibul Islam
+ * Date: 04/05/2023
+ */
+
+/**
+ * @param {number} n
+ * @param {number[][]} edges
+ * @return {number}
+ */
+var countRestrictedPaths = function (n, edges) {
+  const g = Array.from({ length: n + 1 }, () => []);
+  for (let [a, b, c] of edges) {
+    g[a].push([b, c]);
+    g[b].push([a, c]);
+  }
+  // do dijkstras to find shortest path from n to all nodes
+  const dis = new Array(n + 1).fill(Infinity);
+  dis[n] = 0;
+  const dijkstra = () => {
+    const heap = new MinPriorityQueue({ priority: (x) => x[1] });
+    heap.enqueue([n, 0]);
+    while (heap.size()) {
+      const [node, cost] = heap.dequeue().element;
+      for (let [nextNode, w] of g[node]) {
+        const totalCost = cost + w;
+        if (dis[nextNode] > totalCost) {
+          dis[nextNode] = totalCost;
+          heap.enqueue([nextNode, totalCost]);
+        }
+      }
+    }
+  };
+  dijkstra();
+
+  // do dfs from 1 having path always lesser dist
+  let rPaths = 0;
+  const MOD = 1000000007;
+  const dp = new Array(n + 1).fill(-1);
+  const dfs = (curr = 1, rCost = dis[1]) => {
+    if (curr == n) return 1;
+    if (dp[curr] != -1) return dp[curr];
+
+    let op = 0;
+    for (let [n, w] of g[curr]) {
+      if (dis[n] < rCost) {
+        op = (op + dfs(n, dis[n])) % MOD;
+      }
+    }
+
+    return (dp[curr] = op);
+  };
+  return dfs();
+};