2203 - Minimum Weighted Subgraph With the Required Paths.

Hard

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.

You are also given a 2D integer array edges where <code>edgesi = from_i, to_i, weight_i</code> denotes that there exists a directed edge from <code>from_i</code> to <code>to_i</code> with weight <code>weight_i</code>.

Lastly, you are given three distinct integers src1, src2, and dest denoting three distinct nodes of the graph.

Return the minimum weight of a subgraph of the graph such that it is possible to reach dest from both src1 and src2 via a set of edges of this subgraph. In case such a subgraph does not exist, return -1.

A subgraph is a graph whose vertices and edges are subsets of the original graph. The weight of a subgraph is the sum of weights of its constituent edges.

Example 1:

Input: n = 6, edges = \[\[0,2,2],0,5,6,1,0,3,1,4,5,2,1,1,2,3,3,2,3,4,3,4,2,4,5,1], src1 = 0, src2 = 1, dest = 5

Output: 9

Explanation: The above figure represents the input graph. The blue edges represent one of the subgraphs that yield the optimal answer. Note that the subgraph [1,0,3,0,5,6] also yields the optimal answer. It is not possible to get a subgraph with less weight satisfying all the constraints.

Example 2:

Input: n = 3, edges = \[\[0,1,1],2,1,1], src1 = 0, src2 = 1, dest = 2

Output: -1

Explanation: The above figure represents the input graph. It can be seen that there does not exist any path from node 1 to node 2, hence there are no subgraphs satisfying all the constraints.

Constraints:

• <code>3 <= n <= 10⁵</code>

• <code>0 <= edges.length <= 10⁵</code>

• edges[i].length == 3

• <code>0 <= from_i, to_i, src1, src2, dest <= n - 1</code>

• <code>from_i != to_i</code>

• src1, src2, and dest are pairwise distinct.

• <code>1 <= weighti<= 10⁵</code>