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* Articualtion point initial commit
* Refactor the function definitions
* Add introduction comments and helpful links
* Add test for articulation point algorithm
* Inital commit for articulation point test
* Correct test cases
* Rename files to conform to the naming conventions
* Add comments
* Updated Documentation in README.md
* Remove earlier files
* Updated Documentation in README.md
* Rename dfs to ArticulationPointHelper to avoid confusion
* Updated Documentation in README.md
* Make the helper function unexported
* Updated Documentation in README.md
* Refactor the code to avoid global variables
* Updated Documentation in README.md
* Refactor to use structs instead function parameters
* Updated Documentation in README.md
* Restructure comments to compile with project conventions
* Updated Documentation in README.md
* Linting changes
* Reduce comment length and accommodate review comments
* Updated Documentation in README.md
* Updated Documentation in README.md
* Modify function definition to pass graph parameter as a pointer
Co-authored-by: github-action <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Taj <[email protected]>
Co-authored-by: Rak Laptudirm <[email protected]>- Loading branch information
4 people
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Jan 11, 2022
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,100 @@ | ||
| package graph | ||
|
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| import "github.com/TheAlgorithms/Go/math/min" | ||
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| type apHelper struct { | ||
| is_ap []bool | ||
| visited []bool | ||
| child_cnt []int | ||
| discovery_time []int | ||
| earliest_discovery []int | ||
| } | ||
|
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| // ArticulationPoint is a function to identify articulation points in a graph. | ||
| // The function takes the graph as an argument and returns a boolean slice | ||
| // which indicates whether a vertex is an articulation point or not. | ||
| // Worst Case Time Complexity: O(|V| + |E|) | ||
| // Auxiliary Space: O(|V|) | ||
| // reference: https://en.wikipedia.org/wiki/Biconnected_component and https://cptalks.quora.com/Cut-Vertex-Articulation-point | ||
| func ArticulationPoint(graph *Graph) []bool { | ||
| // time variable to keep track of the time of discovery_time of a vertex | ||
| time := 0 | ||
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| //initialize all the variables | ||
| apHelperInstance := &apHelper{ | ||
| is_ap: make([]bool, graph.vertices), | ||
| visited: make([]bool, graph.vertices), | ||
| child_cnt: make([]int, graph.vertices), | ||
| // integer slice to store the discovery time of a vertex as we traverse | ||
| // the graph in a depth first manner | ||
| discovery_time: make([]int, graph.vertices), | ||
| // integer slice to store the earliest discovered vertex reachable from a vertex | ||
| earliest_discovery: make([]int, graph.vertices), | ||
| } | ||
| articulationPointHelper( | ||
| apHelperInstance, | ||
| 0, | ||
| -1, | ||
| &time, | ||
| graph, | ||
| ) | ||
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| if apHelperInstance.child_cnt[0] == 1 { | ||
| // if the root has only one child, it is not an articulation point | ||
| apHelperInstance.is_ap[0] = false | ||
| } | ||
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| return apHelperInstance.is_ap | ||
| } | ||
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| // articulationPointHelper is a recursive function to traverse the graph | ||
| // and mark articulation points. Based on the depth first search transversal | ||
| // of the graph, however modified to keep track and update the | ||
| // `child_cnt`, `discovery_time`` and `earliest_discovery` slices defined above | ||
| func articulationPointHelper( | ||
| apHelperInstance *apHelper, | ||
| vertex int, | ||
| parent int, | ||
| time *int, | ||
| graph *Graph, | ||
| ) { | ||
| apHelperInstance.visited[vertex] = true | ||
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| // Mark the time of discovery of a vertex | ||
| // set the earliest discovery time to the discovered time | ||
| // increment the time | ||
| apHelperInstance.discovery_time[vertex] = *time | ||
| apHelperInstance.earliest_discovery[vertex] = apHelperInstance.discovery_time[vertex] | ||
| *time++ | ||
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| for next_vertex := range graph.edges[vertex] { | ||
| if next_vertex == parent { | ||
| continue | ||
| } | ||
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| if apHelperInstance.visited[next_vertex] { | ||
| apHelperInstance.earliest_discovery[vertex] = min.Int( | ||
| apHelperInstance.earliest_discovery[vertex], | ||
| apHelperInstance.discovery_time[next_vertex], | ||
| ) | ||
| continue | ||
| } | ||
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| apHelperInstance.child_cnt[vertex]++ | ||
| articulationPointHelper( | ||
| apHelperInstance, | ||
| next_vertex, | ||
| vertex, | ||
| time, | ||
| graph, | ||
| ) | ||
| apHelperInstance.earliest_discovery[vertex] = min.Int( | ||
| apHelperInstance.earliest_discovery[vertex], | ||
| apHelperInstance.earliest_discovery[next_vertex], | ||
| ) | ||
| if apHelperInstance.earliest_discovery[next_vertex] >= apHelperInstance.discovery_time[vertex] { | ||
| apHelperInstance.is_ap[vertex] = true | ||
| } | ||
|
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||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,82 @@ | ||
| package graph | ||
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| import ( | ||
| "reflect" | ||
| "testing" | ||
| ) | ||
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| func TestArticulationPoints(t *testing.T) { | ||
| var testCases = []struct { | ||
| description string | ||
| graph Graph | ||
| expected []bool | ||
| }{ | ||
| { | ||
| "Linear tree structure", | ||
| Graph{ | ||
| vertices: 5, | ||
| edges: map[int]map[int]int{ | ||
| 0: { | ||
| 1: 0, | ||
| }, | ||
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| 1: { | ||
| 0: 0, | ||
| 2: 0, | ||
| }, | ||
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| 2: { | ||
| 1: 0, | ||
| 3: 0, | ||
| }, | ||
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| 3: { | ||
| 2: 0, | ||
| 4: 0, | ||
| }, | ||
| }, | ||
| }, | ||
| []bool{false, true, true, true, false}, | ||
| }, { | ||
| "A complete graph", | ||
| Graph{ | ||
| vertices: 4, | ||
| edges: map[int]map[int]int{ | ||
| 0: { | ||
| 1: 0, | ||
| 2: 0, | ||
| 3: 0, | ||
| }, | ||
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| 1: { | ||
| 0: 0, | ||
| 2: 0, | ||
| 3: 0, | ||
| }, | ||
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| 2: { | ||
| 0: 0, | ||
| 1: 0, | ||
| 3: 0, | ||
| }, | ||
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| 3: { | ||
| 0: 0, | ||
| 1: 0, | ||
| 2: 0, | ||
| }, | ||
| }, | ||
| }, | ||
| []bool{false, false, false, false}, | ||
| }, | ||
| } | ||
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| for _, test := range testCases { | ||
| t.Run(test.description, func(t *testing.T) { | ||
| is_ap := ArticulationPoint(&test.graph) | ||
| if !reflect.DeepEqual(is_ap, test.expected) { | ||
| t.Logf("FAIL: %s", test.description) | ||
| } | ||
| }) | ||
| } | ||
| } |