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| 1 | +/** |
| 2 | + * Title: Minimum Weighted Subgraph with the Required Paths |
| 3 | + * 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. |
| 4 | + * Author: Hasibul Islam |
| 5 | + * Date: 04/05/2023 |
| 6 | + */ |
| 7 | + |
| 8 | +/** |
| 9 | + * @param {number} n |
| 10 | + * @param {number[][]} edges |
| 11 | + * @param {number} src1 |
| 12 | + * @param {number} src2 |
| 13 | + * @param {number} dest |
| 14 | + * @return {number} |
| 15 | + */ |
| 16 | +var minimumWeight = function (n, edges, src1, src2, dest) { |
| 17 | + var paths = new Array(n).fill(0).map((i) => []); |
| 18 | + var reversePaths = new Array(n).fill(0).map((i) => []); |
| 19 | + for (var edge of edges) { |
| 20 | + var [u, v, w] = edge; |
| 21 | + paths[u].push([v, w]); |
| 22 | + reversePaths[v].push([u, w]); |
| 23 | + } |
| 24 | + |
| 25 | + var dijkstra = function (start, paths) { |
| 26 | + var visited = []; |
| 27 | + var dp = new Array(n).fill(Number.MAX_SAFE_INTEGER); |
| 28 | + dp[start] = 0; |
| 29 | + |
| 30 | + var pq = new MinPriorityQueue({ priority: (item) => item[1] }); |
| 31 | + pq.enqueue([start, 0]); |
| 32 | + |
| 33 | + while (!pq.isEmpty()) { |
| 34 | + var [u, cost] = pq.dequeue().element; |
| 35 | + if (visited[u] || cost > dp[u]) continue; |
| 36 | + visited[u] = true; |
| 37 | + for (var path of paths[u]) { |
| 38 | + var [v, w] = path; |
| 39 | + if (dp[v] > dp[u] + w) { |
| 40 | + dp[v] = dp[u] + w; |
| 41 | + pq.enqueue([v, dp[v]]); |
| 42 | + } |
| 43 | + } |
| 44 | + } |
| 45 | + |
| 46 | + return dp; |
| 47 | + }; |
| 48 | + |
| 49 | + var dpStartFromSrc1 = dijkstra(src1, paths); |
| 50 | + var dpStartFromSrc2 = dijkstra(src2, paths); |
| 51 | + var dpStartFromDesc = dijkstra(dest, reversePaths); |
| 52 | + |
| 53 | + var ans = Number.MAX_SAFE_INTEGER; |
| 54 | + for (var i = 0; i < n; i++) { |
| 55 | + ans = Math.min( |
| 56 | + ans, |
| 57 | + dpStartFromSrc1[i] + dpStartFromSrc2[i] + dpStartFromDesc[i] |
| 58 | + ); |
| 59 | + } |
| 60 | + |
| 61 | + return ans === Number.MAX_SAFE_INTEGER ? -1 : ans; |
| 62 | +}; |
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