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v/examples/graphs/bellman-ford.v

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/*
A V program for Bellman-Ford's single source
shortest path algorithm.
literaly adapted from:
https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/
// Adapted from this site... from C++ and Python codes
For Portugese reference
http://rascunhointeligente.blogspot.com/2010/10/o-algoritmo-de-bellman-ford-um.html
code by CCS
*/
const large = 999999 // almost inifinity
// a structure to represent a weighted edge in graph
struct EDGE {
mut:
src int
dest int
weight int
}
// building a map of with all edges etc of a graph, represented from a matrix adjacency
// Input: matrix adjacency --> Output: edges list of src, dest and weight
fn build_map_edges_from_graph<T>(g [][]T) map[T]EDGE {
n := g.len // TOTAL OF NODES for this graph -- its dimmension
mut edges_map := map[int]EDGE{} // a graph represented by map of edges
mut edge := 0 // a counter of edges
for i in 0 .. n {
for j in 0 .. n {
// if exist an arc ... include as new edge
if g[i][j] != 0 {
edges_map[edge] = EDGE{i, j, g[i][j]}
edge++
}
}
}
// print('${edges_map}')
return edges_map
}
fn print_sol(dist []int) {
n_vertex := dist.len
print('\n Vertex Distance from Source')
for i in 0 .. n_vertex {
print('\n ${i} --> ${dist[i]}')
}
}
// The main function that finds shortest distances from src
// to all other vertices using Bellman-Ford algorithm. The
// function also detects negative weight cycle
fn bellman_ford<T>(graph [][]T, src int) {
mut edges := build_map_edges_from_graph(graph)
// this function was done to adapt a graph representation
// by a adjacency matrix, to list of adjacency (using a MAP)
n_edges := edges.len // number of EDGES
// Step 1: Initialize distances from src to all other
// vertices as INFINITE
n_vertex := graph.len // adjc matrix ... n nodes or vertex
mut dist := []int{len: n_vertex, init: large} // dist with -1 instead of INIFINITY
// mut path := []int{len: n , init:-1} // previous node of each shortest paht
dist[src] = 0
// Step 2: Relax all edges |V| - 1 times. A simple
// shortest path from src to any other vertex can have
// at-most |V| - 1 edges
for _ in 0 .. n_vertex {
for j in 0 .. n_edges {
mut u := edges[j].src
mut v := edges[j].dest
mut weight := edges[j].weight
if (dist[u] != large) && (dist[u] + weight < dist[v]) {
dist[v] = dist[u] + weight
}
}
}
// Step 3: check for negative-weight cycles. The above
// step guarantees shortest distances if graph doesn't
// contain negative weight cycle. If we get a shorter
// path, then there is a cycle.
for j in 0 .. n_vertex {
mut u := edges[j].src
mut v := edges[j].dest
mut weight := edges[j].weight
if (dist[u] != large) && (dist[u] + weight < dist[v]) {
print('\n Graph contains negative weight cycle')
// If negative cycle is detected, simply
// return or an exit(1)
return
}
}
print_sol(dist)
}
fn main() {
// adjacency matrix = cost or weight
graph_01 := [
[0, -1, 4, 0, 0],
[0, 0, 3, 2, 2],
[0, 0, 0, 0, 0],
[0, 1, 5, 0, 0],
[0, 0, 0, -3, 0],
]
// data from https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/
graph_02 := [
[0, 2, 0, 6, 0],
[2, 0, 3, 8, 5],
[0, 3, 0, 0, 7],
[6, 8, 0, 0, 9],
[0, 5, 7, 9, 0],
]
// data from https://www.geeksforgeeks.org/prims-minimum-spanning-tree-mst-greedy-algo-5/
/*
The graph:
2 3
(0)--(1)--(2)
| / \ |
6| 8/ \5 |7
| / \ |
(3)-------(4)
9
*/
/*
Let us create following weighted graph
From https://www.geeksforgeeks.org/kruskals-minimum-spanning-tree-algorithm-greedy-algo-2/?ref=lbp
10
0--------1
| \ |
6| 5\ |15
| \ |
2--------3
4
*/
graph_03 := [
[0, 10, 6, 5],
[10, 0, 0, 15],
[6, 0, 0, 4],
[5, 15, 4, 0],
]
// To find number of coluns
// mut cols := an_array[0].len
mut graph := [][]int{} // the graph: adjacency matrix
// for index, g_value in [graph_01, graph_02, graph_03] {
for index, g_value in [graph_01, graph_02, graph_03] {
graph = g_value.clone() // graphs_sample[g].clone() // choice your SAMPLE
// allways starting by node 0
start_node := 0
println('\n\n Graph ${index + 1} using Bellman-Ford algorithm (source node: ${start_node})')
bellman_ford(graph, start_node)
}
println('\n BYE -- OK')
}