https://github.com/panagiotiskotsorgios/minimum-weight-subgraph-finder-algorithm
Efficient Java Solution to Compute the Optimal Subgraph in Weighted Directed Graphs
https://github.com/panagiotiskotsorgios/minimum-weight-subgraph-finder-algorithm
algorithms dijkstra graph-algorithms graph-theory java optimization shortest-path weighted-graphs
Last synced: 8 months ago
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Efficient Java Solution to Compute the Optimal Subgraph in Weighted Directed Graphs
- Host: GitHub
- URL: https://github.com/panagiotiskotsorgios/minimum-weight-subgraph-finder-algorithm
- Owner: PanagiotisKotsorgios
- License: mit
- Created: 2024-11-15T21:26:37.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-11-16T15:13:19.000Z (about 1 year ago)
- Last Synced: 2025-04-23T14:36:34.695Z (9 months ago)
- Topics: algorithms, dijkstra, graph-algorithms, graph-theory, java, optimization, shortest-path, weighted-graphs
- Language: Java
- Homepage: https://panagiotiskots.github.io/Website-Java-Algorithm/
- Size: 91.8 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Problem 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.
- 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
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- 0 <= edges.length <= 105
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- edges[i].length == 3
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- 0 <= fromi, toi, src1, src2, dest <= n - 1
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- fromi != toi
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- src1, src2, and dest are pairwise distinct.
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- 1 <= weight[i] <= 105
---
> **Note**: The above problem is based on the [LeetCode 2203. Minimum Weighted Subgraph With the Required Paths](https://leetcode.com/problems/minimum-weighted-subgraph-with-the-required-paths/) problem.
> The entire algorithm was implemented and designed specifically for this [LeetCode problem](https://leetcode.com/problems/minimum-weighted-subgraph-with-the-required-paths/).