ShortestPath

Shortest path problem of an undirected graph from all nodes by Elixir and other languages

Problem statement

Given is an undirected graph with N vertices and M edges. Vertices are in xy-plain. The i-th vertice Vi has a position (Xi, Yi) for visualization of the graph. The j-th edge is connected between Vaj and Vbj has a weight of Wj. Find the shortest path between all vertices.

Constraints

$$ 2 \leq N $$

$$ 1 \leq M \leq \frac{1}{2}N(N-1)$$

$$ 1 \leq i, a, b \leq N$$

$$ 1 \leq j \leq M$$

$$ 1 \leq Wj \leq 1000 $$

Input

Input is given the file in test/support/in in the following format:

N M
X1 Y1
...
XN YN
Va1 Vb1 W1
...
VaM VbM WM

You can use ShortestPath.InputReader.read/1 for obtaining N, M, the list of the lists [Vaj, Vbj, Wj] from the file.

Output

Output the distance Da,b of the shortest path between the vertice Va and Vb for all vertices in the following format, for reducing amount of output:

N
D1,2 D1,3 ... D1,N
D2,3 D2,4 ... D2,N
...
DN-1,N

You can use ShortestPath.OutputWriter.puts/1 for outputing in the above format.

Sample inputs

See the directory test/support/in.

Sample outputs

See the directory test/support/out.

Usage

Run benchmarks

mix run -r bench/shortest_path_bench.exs

If ips and average are 0.50 and 2.00s, respectively, it means time out of the execution.

##### With input N,M = 1000,499500 #####
Name                     ips        average  deviation         median         99th %
Dijkstra.MainA          0.50         2.00 s     ±0.02%         2.00 s         2.00 s

Generate an input case

iex> :rand.seed(:exsss)
iex> ShortestPath.InputCaseGenerator.generate("sample_01.txt", 4, 6) # file_name, n, m

You'll get test/support/in/sample_01.txt.

License

Copyright (c) ShortestPathSolvers 2022

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.