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v/examples/graphs/minimal_spann_tree_prim.v

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/*
Exploring PRIMS,
The data example is from
https://www.geeksforgeeks.org/prims-minimum-spanning-tree-mst-greedy-algo-5/
by CCS
PS: all the pre-requisites of Dijkstra are considered
$ v run file_name.v
Creating a executable
$ v -o an_executable.EXE run file_name.v
$ ./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
shortest path evaluted
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 nodes
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
fn push_pq[T](mut prior_queue []T, data int, priority int) {
mut temp := []T{}
lenght_pq := prior_queue.len
mut i := 0
for (i < lenght_pq) && (priority > prior_queue[i].priority) {
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
for i < lenght_pq {
temp << prior_queue[i]
i++
}
prior_queue = temp.clone() // I am not sure if it the right way
}
// Change the priority of a value/node ... exist a value, change its priority
fn updating_priority[T](mut prior_queue []T, search_data int, new_priority int) {
mut i := 0
mut lenght_pq := prior_queue.len
for i < lenght_pq {
if search_data == prior_queue[i].data {
prior_queue[i] = NODE{search_data, new_priority} // do the copy in the right place
break
}
i++
// all the list was examined
if i >= lenght_pq {
// print('\n Priority Queue: ${prior_queue}')
// print('\n These data ${search_data} and ${new_priority} do not exist ... PRIORITY QUEUE problem\n')
// if it does not find ... then push it
push_pq(mut prior_queue, search_data, new_priority)
// exit(1) // panic(s string)
}
} // end for
}
// a single departure or remove from queue
fn departure_priority[T](mut prior_queue []T) int {
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
fn all_adjacents[T](g [][]T, v int) []int {
mut temp := []int{}
for i in 0 .. (g.len) {
if g[v][i] > 0 {
temp << i
}
}
return temp
}
// print the costs from origin up to all nodes
// A utility function to print the
// constructed MST stored in parent[]
// print all paths and their cost or weight
fn print_solution(path []int, g [][]int) {
// print(' PATH: ${path} ==> ${path.len}')
print(' Edge \tWeight\n')
mut sum := 0
for node in 0 .. (path.len) {
if path[node] == -1 {
print('\n ${node} <== reference or start node')
} else {
print('\n ${node} <--> ${path[node]} \t${g[node][path[node]]}')
sum += g[node][path[node]]
}
}
print('\n Minimum Cost Spanning Tree: ${sum}\n\n')
}
// check structure from: https://www.geeksforgeeks.org/dijkstras-shortest-path-algorithm-greedy-algo-7/
// s: source for all nodes
// Two results are obtained ... cost and paths
fn prim_mst(g [][]int, s int) {
mut pq_queue := []NODE{} // creating a priority queue
push_pq(mut pq_queue, s, 0) // goes s with priority 0
mut n := g.len
mut dist := []int{len: n, init: -1} // dist with -1 instead of INIFINITY
mut path := []int{len: n, init: -1} // previous node of each shortest paht
// Distance of source vertex from itself is always 0
dist[s] = 0
for pq_queue.len != 0 {
mut v := departure_priority(mut pq_queue)
// for all W adjcents vertices of v
mut adjs_of_v := all_adjacents(g, v) // all_ADJ of v ....
// print('\n :${dist} :: ${pq_queue}')
// 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] = g[v][w]
push_pq(mut pq_queue, w, dist[w])
path[w] = v // collecting the previous node -- lowest weight
}
if dist[w] > new_dist {
dist[w] = g[v][w] // new_dist//
updating_priority(mut pq_queue, w, dist[w])
path[w] = v // father / previous node
}
}
}
// print('\n \n Previous node of shortest path: ${path}')
// print_paths_dist(path , dist)
print_solution(path, g)
}
/*
Solution Expected graph_02
Edge Weight
0 - 1 2
1 - 2 3
0 - 3 6
1 - 4 5
*/
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],
]
// 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] {
println('\n Minimal Spanning Tree of graph ${index + 1} using PRIM algorithm')
graph = g_value.clone() // graphs_sample[g].clone() // choice your SAMPLE
// starting by node x ... see the graphs dimmension
start_node := 0
prim_mst(graph, start_node)
}
println('\n BYE -- OK')
}