2022-06-02 07:11:29 +03:00
|
|
|
/*
|
|
|
|
Exploring Dijkstra,
|
|
|
|
The data example is from
|
|
|
|
https://www.geeksforgeeks.org/dijkstras-shortest-path-algorithm-greedy-algo-7/
|
|
|
|
|
|
|
|
by CCS
|
|
|
|
Dijkstra's single source shortest path algorithm.
|
|
|
|
The program uses an adjacency matrix representation of a graph
|
|
|
|
|
|
|
|
This Dijkstra algorithm uses a priority queue to save
|
|
|
|
the shortest paths. The queue structure has a data
|
|
|
|
which is the number of the node,
|
|
|
|
and the priority field which is the shortest distance.
|
|
|
|
|
|
|
|
PS: all the pre-requisites of Dijkstra are considered
|
|
|
|
|
|
|
|
$ v run file_name.v
|
|
|
|
// Creating a executable
|
|
|
|
$ v run file_name.v -o an_executable.EXE
|
|
|
|
$ ./an_executable.EXE
|
|
|
|
|
|
|
|
Code based from : Data Structures and Algorithms Made Easy: Data Structures and Algorithmic Puzzles, Fifth Edition (English Edition)
|
|
|
|
pseudo code written in C
|
|
|
|
This idea is quite different: it uses a priority queue to store the current
|
2023-05-25 16:54:46 +03:00
|
|
|
shortest path evaluated
|
2022-06-02 07:11:29 +03:00
|
|
|
The priority queue structure built using a list to simulate
|
|
|
|
the queue. A heap is not used in this case.
|
|
|
|
*/
|
|
|
|
|
|
|
|
// a structure
|
|
|
|
struct NODE {
|
|
|
|
mut:
|
|
|
|
data int // NUMBER OF NODE
|
|
|
|
priority int // Lower values priority indicate ==> higher priority
|
|
|
|
}
|
|
|
|
|
|
|
|
// Function to push according to priority ... the lower priority is goes ahead
|
|
|
|
// The "push" always sorted in pq
|
2022-11-26 19:23:26 +03:00
|
|
|
fn push_pq[T](mut prior_queue []T, data int, priority int) {
|
2022-06-02 07:11:29 +03:00
|
|
|
mut temp := []T{}
|
2023-05-25 16:54:46 +03:00
|
|
|
pq_len := prior_queue.len
|
2022-06-02 07:11:29 +03:00
|
|
|
|
|
|
|
mut i := 0
|
2023-05-25 16:54:46 +03:00
|
|
|
for i < pq_len && priority > prior_queue[i].priority {
|
2022-06-02 07:11:29 +03:00
|
|
|
temp << prior_queue[i]
|
|
|
|
i++
|
|
|
|
}
|
|
|
|
// INSERTING SORTED in the queue
|
|
|
|
temp << NODE{data, priority} // do the copy in the right place
|
|
|
|
// copy the another part (tail) of original prior_queue
|
2023-05-25 16:54:46 +03:00
|
|
|
for i < pq_len {
|
2022-06-02 07:11:29 +03:00
|
|
|
temp << prior_queue[i]
|
|
|
|
i++
|
|
|
|
}
|
|
|
|
prior_queue = temp.clone() // I am not sure if it the right way
|
|
|
|
// IS IT THE RIGHT WAY?
|
|
|
|
}
|
|
|
|
|
|
|
|
// Change the priority of a value/node ... exist a value, change its priority
|
2022-11-26 19:23:26 +03:00
|
|
|
fn updating_priority[T](mut prior_queue []T, search_data int, new_priority int) {
|
2022-06-02 07:11:29 +03:00
|
|
|
mut i := 0
|
2023-05-25 16:54:46 +03:00
|
|
|
mut pq_len := prior_queue.len
|
2022-06-02 07:11:29 +03:00
|
|
|
|
2023-05-25 16:54:46 +03:00
|
|
|
for i < pq_len {
|
2022-06-02 07:11:29 +03:00
|
|
|
if search_data == prior_queue[i].data {
|
2023-05-25 16:54:46 +03:00
|
|
|
prior_queue[i] = NODE{search_data, new_priority} // do the copy in the right place
|
2022-06-02 07:11:29 +03:00
|
|
|
break
|
|
|
|
}
|
|
|
|
i++
|
|
|
|
// all the list was examined
|
2023-05-25 16:54:46 +03:00
|
|
|
if i >= pq_len {
|
2022-11-15 16:53:13 +03:00
|
|
|
print('\n This data ${search_data} does exist ... PRIORITY QUEUE problem\n')
|
2022-06-02 07:11:29 +03:00
|
|
|
exit(1) // panic(s string)
|
|
|
|
}
|
|
|
|
} // end for
|
|
|
|
}
|
|
|
|
|
|
|
|
// a single departure or remove from queue
|
2022-11-26 19:23:26 +03:00
|
|
|
fn departure_priority[T](mut prior_queue []T) int {
|
2022-06-02 07:11:29 +03:00
|
|
|
mut x := prior_queue[0].data
|
|
|
|
prior_queue.delete(0) // or .delete_many(0, 1 )
|
|
|
|
return x
|
|
|
|
}
|
|
|
|
|
|
|
|
// give a NODE v, return a list with all adjacents
|
|
|
|
// Take care, only positive EDGES
|
2022-11-26 19:23:26 +03:00
|
|
|
fn all_adjacents[T](g [][]T, v int) []int {
|
2022-07-08 15:35:45 +03:00
|
|
|
mut temp := []int{}
|
2022-06-02 07:11:29 +03:00
|
|
|
for i in 0 .. (g.len) {
|
|
|
|
if g[v][i] > 0 {
|
|
|
|
temp << i
|
|
|
|
}
|
|
|
|
}
|
|
|
|
return temp
|
|
|
|
}
|
|
|
|
|
|
|
|
// print the costs from origin up to all nodes
|
2022-11-26 19:23:26 +03:00
|
|
|
fn print_solution[T](dist []T) {
|
2022-06-02 07:11:29 +03:00
|
|
|
print('Vertex \tDistance from Source')
|
|
|
|
for node in 0 .. (dist.len) {
|
2022-11-15 16:53:13 +03:00
|
|
|
print('\n ${node} ==> \t ${dist[node]}')
|
2022-06-02 07:11:29 +03:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// print all paths and their cost or weight
|
2022-11-26 19:23:26 +03:00
|
|
|
fn print_paths_dist[T](path []T, dist []T) {
|
2022-06-02 07:11:29 +03:00
|
|
|
print('\n Read the nodes from right to left (a path): \n')
|
|
|
|
|
|
|
|
for node in 1 .. (path.len) {
|
2022-11-15 16:53:13 +03:00
|
|
|
print('\n ${node} ')
|
2022-06-02 07:11:29 +03:00
|
|
|
mut i := node
|
|
|
|
for path[i] != -1 {
|
|
|
|
print(' <= ${path[i]} ')
|
|
|
|
i = path[i]
|
|
|
|
}
|
|
|
|
print('\t PATH COST: ${dist[node]}')
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// check structure from: https://www.geeksforgeeks.org/dijkstras-shortest-path-algorithm-greedy-algo-7/
|
|
|
|
// s: source for all nodes
|
|
|
|
// Two results are obtained ... cost and paths
|
|
|
|
fn dijkstra(g [][]int, s int) {
|
|
|
|
mut pq_queue := []NODE{} // creating a priority queue
|
|
|
|
push_pq(mut pq_queue, s, 0) // goes s with priority 0
|
|
|
|
mut n := g.len
|
|
|
|
|
|
|
|
mut dist := []int{len: n, init: -1} // dist with -1 instead of INIFINITY
|
2023-05-25 16:54:46 +03:00
|
|
|
mut path := []int{len: n, init: -1} // previous node of each shortest path
|
2022-06-02 07:11:29 +03:00
|
|
|
|
|
|
|
// Distance of source vertex from itself is always 0
|
|
|
|
dist[s] = 0
|
|
|
|
|
|
|
|
for pq_queue.len != 0 {
|
|
|
|
mut v := departure_priority(mut pq_queue)
|
|
|
|
// for all W adjcents vertices of v
|
|
|
|
mut adjs_of_v := all_adjacents(g, v) // all_ADJ of v ....
|
|
|
|
// print('\n ADJ ${v} is ${adjs_of_v}')
|
|
|
|
mut new_dist := 0
|
|
|
|
for w in adjs_of_v {
|
|
|
|
new_dist = dist[v] + g[v][w]
|
|
|
|
if dist[w] == -1 {
|
|
|
|
dist[w] = new_dist
|
|
|
|
push_pq(mut pq_queue, w, dist[w])
|
|
|
|
path[w] = v // collecting the previous node -- lowest weight
|
|
|
|
}
|
|
|
|
if dist[w] > new_dist {
|
|
|
|
dist[w] = new_dist
|
|
|
|
updating_priority(mut pq_queue, w, dist[w])
|
2022-07-08 15:35:45 +03:00
|
|
|
path[w] = v
|
2022-06-02 07:11:29 +03:00
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// print the constructed distance array
|
|
|
|
print_solution(dist)
|
|
|
|
// print('\n \n Previous node of shortest path: ${path}')
|
|
|
|
print_paths_dist(path, dist)
|
|
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
|
|
Solution Expected
|
|
|
|
Vertex Distance from Source
|
|
|
|
0 0
|
|
|
|
1 4
|
|
|
|
2 12
|
|
|
|
3 19
|
|
|
|
4 21
|
|
|
|
5 11
|
|
|
|
6 9
|
|
|
|
7 8
|
|
|
|
8 14
|
|
|
|
*/
|
|
|
|
|
|
|
|
fn main() {
|
|
|
|
// adjacency matrix = cost or weight
|
|
|
|
graph_01 := [
|
|
|
|
[0, 4, 0, 0, 0, 0, 0, 8, 0],
|
|
|
|
[4, 0, 8, 0, 0, 0, 0, 11, 0],
|
|
|
|
[0, 8, 0, 7, 0, 4, 0, 0, 2],
|
|
|
|
[0, 0, 7, 0, 9, 14, 0, 0, 0],
|
|
|
|
[0, 0, 0, 9, 0, 10, 0, 0, 0],
|
|
|
|
[0, 0, 4, 14, 10, 0, 2, 0, 0],
|
|
|
|
[0, 0, 0, 0, 0, 2, 0, 1, 6],
|
|
|
|
[8, 11, 0, 0, 0, 0, 1, 0, 7],
|
|
|
|
[0, 0, 2, 0, 0, 0, 6, 7, 0],
|
|
|
|
]
|
|
|
|
|
|
|
|
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],
|
|
|
|
]
|
|
|
|
|
2023-05-25 16:54:46 +03:00
|
|
|
// To find number of columns
|
2022-06-02 07:11:29 +03:00
|
|
|
// 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
|
2023-05-25 16:54:46 +03:00
|
|
|
// always starting by node 0
|
2022-06-02 07:11:29 +03:00
|
|
|
start_node := 0
|
2022-11-15 16:53:13 +03:00
|
|
|
println('\n\n Graph ${index + 1} using Dijkstra algorithm (source node: ${start_node})')
|
2022-06-02 07:11:29 +03:00
|
|
|
dijkstra(graph, start_node)
|
|
|
|
}
|
|
|
|
|
|
|
|
println('\n BYE -- OK')
|
|
|
|
}
|