examples: 2 new examples for graph algorithms (topological sorting) (#14303)
Claudio Cesar de Sá
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// https://en.wikipedia.org/wiki/Topological_sorting
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// A DFS RECURSIVE ALGORITHM ....
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// An alternative algorithm for topological sorting is based on depth-first search. The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning
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// of the topological sort or the node has no outgoing edges (i.e. a leaf node)
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// Discussion: https://www.gatevidyalay.com/topological-sort-topological-sorting/
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// $ v run dfs_topological_ordering.v
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// Author: CCS
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// THE DFS RECURSIVE .... classical searchig for leaves nodes
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// the arguments are used in the function to avoid global variables....
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fn dfs_recursive(u string, mut visited map[string]bool, graph map[string][]string, mut top_sorting []string) {
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print(' Visiting: $u -> ')
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visited[u] = true
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for v in graph[u] {
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if visited[v] == false {
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dfs_recursive(v, mut visited, graph, mut top_sorting)
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}
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}
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top_sorting << u
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}
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// Creating aa map to initialize with of visited nodes .... all with false in the init
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// so these nodes are NOT VISITED YET
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fn visited_init(a_graph map[string][]string) map[string]bool {
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mut array_of_keys := a_graph.keys() // get all keys of this map
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mut temp := map[string]bool{} // attention in these initializations with maps
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for i in array_of_keys {
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temp[i] = false
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}
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return temp
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}
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// attention here a map STRING ---> ONE BOOLEAN ... not a string
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fn main() {
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// A map illustration to use in a graph
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// the graph: adjacency matrix
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graph_01 := {
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'A': ['C', 'B']
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'B': ['D']
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'C': ['D']
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'D': []
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}
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graph_02 := {
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'A': ['B', 'C', 'D']
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'B': ['E']
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'C': ['F']
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'D': ['G']
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'E': ['H']
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'F': ['H']
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'G': ['H']
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'H': [] // no cycles
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}
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// from: https://en.wikipedia.org/wiki/Topological_sorting
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graph_03 := {
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'5': ['11']
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'7': ['11', '8']
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'3': ['8', '10']
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'11': ['2', '9', '10']
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'8': ['9']
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'2': []
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'9': []
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'10': []
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}
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mut graph := map[string][]string{} // the graph: adjacency matrix
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for index, g_value in [graph_01, graph_02, graph_03] {
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println('Topological sorting for the graph $index using a DFS recursive')
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graph = g_value.clone() // graphs_sample[g].clone() // choice your SAMPLE
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// mut n_nodes := graph.len
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mut visited := visited_init(graph) // a map with nodes not visited
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// mut start := (graph.keys()).first() // arbitrary, any node if you wish
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mut top_sorting := []string{}
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// advantages of map ... getting all nodes
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for i in graph.keys() {
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if visited[i] != true {
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dfs_recursive(i, mut visited, graph, mut top_sorting)
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}
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}
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print('\n A topological sorting of graph $index : ')
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// println(g_value)
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println(top_sorting.reverse())
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println('')
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} // End of for
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}
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@ -0,0 +1,146 @@
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// The idea of this algorithm follow :
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// https://www.gatevidyalay.com/topological-sort-topological-sorting/ (GREEDY)
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// (no cycles are detected)
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// https://en.wikipedia.org/wiki/Topological_sorting ... just the input data
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// and the Kahn algorithm
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// Author: CCS
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// the idea is rude: https://www.gatevidyalay.com/topological-sort-topological-sorting/
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fn topog_sort_greedy(graph map[string][]string) []string {
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n_nodes := graph.len // numbers of nodes of this graph
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mut top_order := []string{} // a vector with sequence of nodes visited
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mut count := 0
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/*
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IDEA ( a greedy algorythm ):
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1. choose allways the node with smallest input degree
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2. visit it
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3. put it in the output vector
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4. remove it from graph
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5. update the graph (a new graph)
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6. find a new vector degree
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7. until all nodes has been visited
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Back to step 1 (used the variable count)
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Maybe it seems the Kahn's algorithm
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*/
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mut v_degree := in_degree(graph) // return: map [string] int
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print('V Degree $v_degree')
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mut small_degree := min_degree(v_degree)
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mut new_graph := remove_node_from_graph(small_degree, graph)
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top_order << small_degree
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count++
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for (count < n_nodes) {
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v_degree = in_degree(new_graph) // return: map [string] int
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print('\nV Degree $v_degree')
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small_degree = min_degree(v_degree)
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new_graph = remove_node_from_graph(small_degree, new_graph)
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top_order << small_degree
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count++
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}
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// print("\n New Graph ${new_graph}")
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return top_order
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}
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// Give a node, return a list with all nodes incidents or fathers of this node
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fn all_fathers(node string, a_map map[string][]string) []string {
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mut array_of_keys := a_map.keys() // get a key of this map
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mut all_incident := []string{}
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for i in array_of_keys {
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// in : function
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if node in a_map[i] {
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all_incident << i // a queue of this search
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}
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}
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return all_incident
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}
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// Input: a map with input degree values, return the key with smallest value
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fn min_degree(a_map map[string]int) string {
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mut array_of_keys := a_map.keys() // get a key of this map
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mut key_min := array_of_keys.first()
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mut val_min := a_map[key_min]
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// print("\n MIN: ${val_min} \t key_min: ${key_min} \n the map inp_degree: ${a_map}")
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for i in array_of_keys {
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// there is a smaller
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if val_min > a_map[i] {
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val_min = a_map[i]
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key_min = i
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}
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}
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return key_min // the key with smallest value
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}
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// Given a graph ... return a list of integer with degree of each node
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fn in_degree(a_map map[string][]string) map[string]int {
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mut array_of_keys := a_map.keys() // get a key of this map
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// print(array_of_keys)
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mut degree := map[string]int{}
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for i in array_of_keys {
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degree[i] = all_fathers(i, a_map).len
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}
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// print("\n Degree ${in_degree}" )
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return degree // a vector of the indegree graph
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}
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// REMOVE A NODE FROM A GRAPH AND RETURN ANOTHER GRAPH
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fn remove_node_from_graph(node string, a_map map[string][]string) map[string][]string {
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// mut new_graph := map [string] string {}
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mut new_graph := a_map.clone() // copy the graph
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new_graph.delete(node)
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mut all_nodes := new_graph.keys() // get all nodes of this graph
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// FOR THE FUTURE with filter
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// for i in all_nodes {
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// new_graph[i] = new_graph[i].filter(index(it) != node)
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// }
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// A HELP FROM V discussion GITHUB - thread
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for key in all_nodes {
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i := new_graph[key].index(node)
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if i >= 0 {
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new_graph[key].delete(i)
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}
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}
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// print("\n NEW ${new_graph}" )
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return new_graph
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}
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fn main() {
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// A map illustration to use in a graph
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// adjacency matrix
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graph_01 := {
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'A': ['C', 'B']
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'B': ['D']
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'C': ['D']
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'D': []
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}
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graph_02 := {
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'A': ['B', 'C', 'D']
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'B': ['E']
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'C': ['F']
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'D': ['G']
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'E': ['H']
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'F': ['H']
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'G': ['H']
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'H': []
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}
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// from: https://en.wikipedia.org/wiki/Topological_sorting
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graph_03 := {
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'5': ['11']
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'7': ['11', '8']
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'3': ['8', '10']
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'11': ['2', '9', '10']
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'8': ['9']
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'2': []
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'9': []
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'10': []
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}
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println('\nA Topological Sort of G1: ${topog_sort_greedy(graph_01)}')
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println('\nA Topological Sort of G2: ${topog_sort_greedy(graph_02)}')
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println('\nA Topological Sort of G3: ${topog_sort_greedy(graph_03)}')
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// ['2', '9', '10', '11', '5', '8', '7', '3']
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}
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