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examples: some new graphs algorithms and improving 2 others (#14556)

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Claudio Cesar de Sá 2022-06-02 01:11:29 -03:00 committed by GitHub
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163
examples/graphs/bellman-ford.v 100644
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@ -0,0 +1,163 @@
/*
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
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')
}
//=================================================

31
examples/graphs/bfs2.v
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@ -1,4 +1,4 @@
// Author: ccs
// Author: CCS
// I follow literally code in C, done many years ago
fn main() {
// Adjacency matrix as a map
@ -20,10 +20,9 @@ fn breadth_first_search_path(graph map[string][]string, start string, target str
mut path := []string{} // ONE PATH with SUCCESS = array
mut queue := []string{} // a queue ... many paths
// all_nodes := graph.keys() // get a key of this map
n_nodes := graph.len // numbers of nodes of this graph
// a map to store all the nodes visited to avoid cycles
// start all them with False, not visited yet
mut visited := a_map_nodes_bool(n_nodes) // a map fully
mut visited := visited_init(graph) // a map fully
// false ==> not visited yet: {'A': false, 'B': false, 'C': false, 'D': false, 'E': false}
queue << start // first arrival
for queue.len != 0 {
@ -51,19 +50,6 @@ fn breadth_first_search_path(graph map[string][]string, start string, target str
return path
}
// Creating a map for VISITED nodes ...
// starting by false ===> means this node was not visited yet
fn a_map_nodes_bool(size int) map[string]bool {
mut my_map := map[string]bool{} // look this map ...
base := u8(65)
mut key := base.ascii_str()
for i in 0 .. size {
key = u8(base + i).ascii_str()
my_map[key] = false
}
return my_map
}
// classical removing of a node from the start of a queue
fn departure(mut queue []string) string {
mut x := queue[0]
@ -71,6 +57,17 @@ fn departure(mut queue []string) string {
return x
}
// Creating aa map to initialize with of visited nodes .... all with false in the init
// so these nodes are NOT VISITED YET
fn visited_init(a_graph map[string][]string) map[string]bool {
mut array_of_keys := a_graph.keys() // get all keys of this map
mut temp := map[string]bool{} // attention in these initializations with maps
for i in array_of_keys {
temp[i] = false
}
return temp
}
// Based in the current node that is final, search for its parent, already visited, up to the root or start node
fn build_path_reverse(graph map[string][]string, start string, final string, visited map[string]bool) []string {
print('\n\n Nodes visited (true) or no (false): $visited')
@ -90,3 +87,5 @@ fn build_path_reverse(graph map[string][]string, start string, final string, vis
}
return path
}
//======================================================

22
examples/graphs/dfs.v
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@ -1,4 +1,4 @@
// Author: ccs
// Author: CCS
// I follow literally code in C, done many years ago
fn main() {
@ -35,8 +35,7 @@ fn depth_first_search_path(graph map[string][]string, start string, target strin
mut path := []string{} // ONE PATH with SUCCESS = array
mut stack := []string{} // a stack ... many nodes
// all_nodes := graph.keys() // get a key of this map
n_nodes := graph.len // numbers of nodes of this graph
mut visited := a_map_nodes_bool(n_nodes) // a map fully
mut visited := visited_init(graph) // a map fully with false in all vertex
// false ... not visited yet: {'A': false, 'B': false, 'C': false, 'D': false, 'E': false}
stack << start // first push on the stack
@ -72,14 +71,15 @@ fn depth_first_search_path(graph map[string][]string, start string, target strin
return path
}
// Creating a map for nodes not VISITED visited ...
// starting by false ===> means this node was not visited yet
fn a_map_nodes_bool(size int) map[string]bool {
mut my_map := map[string]bool{} // look this map ...
for i in 0 .. size {
my_map[u8(65 + i).ascii_str()] = false
// Creating aa map to initialize with of visited nodes .... all with false in the init
// so these nodes are NOT VISITED YET
fn visited_init(a_graph map[string][]string) map[string]bool {
mut array_of_keys := a_graph.keys() // get all keys of this map
mut temp := map[string]bool{} // attention in these initializations with maps
for i in array_of_keys {
temp[i] = false
}
return my_map
return temp
}
// Based in the current node that is final, search for his parent, that is already visited, up to the root or start node
@ -101,3 +101,5 @@ fn build_path_reverse(graph map[string][]string, start string, final string, vis
}
return path
}
//*****************************************************

241
examples/graphs/dijkstra.v 100644
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@ -0,0 +1,241 @@
/*
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
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 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
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
// IS 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 This data $search_data does exist ... PRIORITY QUEUE problem\n')
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
fn print_solution<T>(dist []T) {
print('Vertex \tDistance from Source')
for node in 0 .. (dist.len) {
print('\n $node ==> \t ${dist[node]}')
}
}
// print all paths and their cost or weight
fn print_paths_dist<T>(path []T, dist []T) {
print('\n Read the nodes from right to left (a path): \n')
for node in 1 .. (path.len) {
print('\n $node ')
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
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 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])
path[w] = v //
}
}
}
// 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],
]
// 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 Dijkstra algorithm (source node: $start_node)')
dijkstra(graph, start_node)
}
println('\n BYE -- OK')
}
//********************************************************************

230
examples/graphs/minimal_spann_tree_prim.v 100644
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@ -0,0 +1,230 @@
/*
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 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
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
// IS 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')
}
//********************************************************************