Minimum Weighted Subgraph with the Required Paths problem solved

Author: hasibulislam999

Shortest Path/2203_minimum-weighted-subgraph-with-the-required-paths.js

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+/**
+ * Title: Minimum Weighted Subgraph with the Required Paths
+ * Description: You are given an integer n denoting the number of nodes of a weighted directed graph. The nodes are numbered from 0 to n - 1.
+ * Author: Hasibul Islam
+ * Date: 04/05/2023
+ */
+
+/**
+ * @param {number} n
+ * @param {number[][]} edges
+ * @param {number} src1
+ * @param {number} src2
+ * @param {number} dest
+ * @return {number}
+ */
+var minimumWeight = function (n, edges, src1, src2, dest) {
+  var paths = new Array(n).fill(0).map((i) => []);
+  var reversePaths = new Array(n).fill(0).map((i) => []);
+  for (var edge of edges) {
+    var [u, v, w] = edge;
+    paths[u].push([v, w]);
+    reversePaths[v].push([u, w]);
+  }
+
+  var dijkstra = function (start, paths) {
+    var visited = [];
+    var dp = new Array(n).fill(Number.MAX_SAFE_INTEGER);
+    dp[start] = 0;
+
+    var pq = new MinPriorityQueue({ priority: (item) => item[1] });
+    pq.enqueue([start, 0]);
+
+    while (!pq.isEmpty()) {
+      var [u, cost] = pq.dequeue().element;
+      if (visited[u] || cost > dp[u]) continue;
+      visited[u] = true;
+      for (var path of paths[u]) {
+        var [v, w] = path;
+        if (dp[v] > dp[u] + w) {
+          dp[v] = dp[u] + w;
+          pq.enqueue([v, dp[v]]);
+        }
+      }
+    }
+
+    return dp;
+  };
+
+  var dpStartFromSrc1 = dijkstra(src1, paths);
+  var dpStartFromSrc2 = dijkstra(src2, paths);
+  var dpStartFromDesc = dijkstra(dest, reversePaths);
+
+  var ans = Number.MAX_SAFE_INTEGER;
+  for (var i = 0; i < n; i++) {
+    ans = Math.min(
+      ans,
+      dpStartFromSrc1[i] + dpStartFromSrc2[i] + dpStartFromDesc[i]
+    );
+  }
+
+  return ans === Number.MAX_SAFE_INTEGER ? -1 : ans;
+};