Package g2201_2300.s2203_minimum_weighted_subgraph_with_the_required_paths

Class Solution

java.lang.Object

g2201_2300.s2203_minimum_weighted_subgraph_with_the_required_paths.Solution

public class Solution
extends Object

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 edges[i] = [fromi, toi, weighti] denotes that there exists a **directed** edge from fromi to toi with weight weighti. 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:** * 3 <= n <= 105 * 0 <= edges.length <= 105 * `edges[i].length == 3` * 0 <= fromi, toi, src1, src2, dest <= n - 1 * fromi != toi * `src1`, `src2`, and `dest` are pairwise distinct. * 1 <= weight[i] <= 105

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
long	minimumWeight(int n, int[][] edges, int src1, int src2, int dest)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Solution

public Solution()

Method Details

minimumWeight

public long minimumWeight(int n,
 int[][] edges,
 int src1,
 int src2,
 int dest)