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Graphs articulation points (#452)
* 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]>
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‎README.md

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@@ -390,16 +390,17 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
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---
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##### Functions:
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1. [`BreadthFirstSearch`](./graph/breadthfirstsearch.go#L9): BreadthFirstSearch is an algorithm for traversing and searching graph data structures. It starts at an arbitrary node of a graph, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. Worst-case performance O(|V|+|E|)=O(b^{d})}O(|V|+|E|)=O(b^{d}) Worst-case space complexity O(|V|)=O(b^{d})}O(|V|)=O(b^{d}) reference: https://en.wikipedia.org/wiki/Breadth-first_search
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2. [`DepthFirstSearch`](./graph/depthfirstsearch.go#L53): No description provided.
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3. [`DepthFirstSearchHelper`](./graph/depthfirstsearch.go#L21): No description provided.
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4. [`FloydWarshall`](./graph/floydwarshall.go#L15): FloydWarshall Returns all pair's shortest path using Floyd Warshall algorithm
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5. [`GetIdx`](./graph/depthfirstsearch.go#L3): No description provided.
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6. [`KruskalMST`](./graph/kruskal.go#L87): KruskalMST will return a minimum spanning tree along with its total cost to using Kruskal's algorithm. Time complexity is O(m * log (n)) where m is the number of edges in the graph and n is number of nodes in it.
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7. [`New`](./graph/graph.go#L16): Constructor functions for graphs (undirected by default)
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8. [`NewDSU`](./graph/kruskal.go#L34): NewDSU will return an initialised DSU using the value of n which will be treated as the number of elements out of which the DSU is being made
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9. [`NotExist`](./graph/depthfirstsearch.go#L12): No description provided.
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10. [`Topological`](./graph/topological.go#L7): Assumes that graph given is valid and possible to get a topo ordering. constraints are array of []int{a, b}, representing an edge going from a to b
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1. [`ArticulationPoint`](./graph/articulationpoints.go#L19): 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
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2. [`BreadthFirstSearch`](./graph/breadthfirstsearch.go#L9): BreadthFirstSearch is an algorithm for traversing and searching graph data structures. It starts at an arbitrary node of a graph, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. Worst-case performance O(|V|+|E|)=O(b^{d})}O(|V|+|E|)=O(b^{d}) Worst-case space complexity O(|V|)=O(b^{d})}O(|V|)=O(b^{d}) reference: https://en.wikipedia.org/wiki/Breadth-first_search
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3. [`DepthFirstSearch`](./graph/depthfirstsearch.go#L53): No description provided.
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4. [`DepthFirstSearchHelper`](./graph/depthfirstsearch.go#L21): No description provided.
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5. [`FloydWarshall`](./graph/floydwarshall.go#L15): FloydWarshall Returns all pair's shortest path using Floyd Warshall algorithm
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6. [`GetIdx`](./graph/depthfirstsearch.go#L3): No description provided.
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7. [`KruskalMST`](./graph/kruskal.go#L87): KruskalMST will return a minimum spanning tree along with its total cost to using Kruskal's algorithm. Time complexity is O(m * log (n)) where m is the number of edges in the graph and n is number of nodes in it.
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8. [`New`](./graph/graph.go#L16): Constructor functions for graphs (undirected by default)
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9. [`NewDSU`](./graph/kruskal.go#L34): NewDSU will return an initialised DSU using the value of n which will be treated as the number of elements out of which the DSU is being made
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10. [`NotExist`](./graph/depthfirstsearch.go#L12): No description provided.
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11. [`Topological`](./graph/topological.go#L7): Assumes that graph given is valid and possible to get a topo ordering. constraints are array of []int{a, b}, representing an edge going from a to b
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---
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##### Types
@@ -605,6 +606,7 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
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##### Functions:
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1. [`IsPalindrome`](./strings/palindrome/ispalindrome.go#L26): No description provided.
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2. [`IsPalindromeRecursive`](./strings/palindrome/ispalindrome.go#L39): No description provided.
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---
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</details><details>
@@ -836,14 +838,15 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
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4. [`HeapSort`](./sort/heapsort.go#L121): No description provided.
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5. [`ImprovedSimpleSort`](./sort/simplesort.go#L25): ImprovedSimpleSort is a improve SimpleSort by skipping an unnecessary comparison of the first and last. This improved version is more similar to implementation of insertion sort
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6. [`InsertionSort`](./sort/insertionsort.go#L3): No description provided.
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7. [`Mergesort`](./sort/mergesort.go#L35): Mergesort Perform mergesort on a slice of ints
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8. [`Pigeonhole`](./sort/pigeonholesort.go#L12): Pigeonhole sorts a slice using pigeonhole sorting algorithm.
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9. [`QuickSort`](./sort/quicksort.go#L37): QuickSort Sorts the entire array
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10. [`QuickSortRange`](./sort/quicksort.go#L24): QuickSortRange Sorts the specified range within the array
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11. [`RadixSort`](./sort/radixsort.go#L35): No description provided.
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12. [`SelectionSort`](./sort/selectionsort.go#L3): No description provided.
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13. [`ShellSort`](./sort/shellsort.go#L3): No description provided.
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14. [`SimpleSort`](./sort/simplesort.go#L11): No description provided.
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7. [`MergeIter`](./sort/mergesort.go#L51): No description provided.
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8. [`Mergesort`](./sort/mergesort.go#L37): Mergesort Perform mergesort on a slice of ints
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9. [`Pigeonhole`](./sort/pigeonholesort.go#L12): Pigeonhole sorts a slice using pigeonhole sorting algorithm.
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10. [`QuickSort`](./sort/quicksort.go#L37): QuickSort Sorts the entire array
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11. [`QuickSortRange`](./sort/quicksort.go#L24): QuickSortRange Sorts the specified range within the array
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12. [`RadixSort`](./sort/radixsort.go#L35): No description provided.
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13. [`SelectionSort`](./sort/selectionsort.go#L3): No description provided.
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14. [`ShellSort`](./sort/shellsort.go#L3): No description provided.
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15. [`SimpleSort`](./sort/simplesort.go#L11): No description provided.
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---
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##### Types

‎graph/articulationpoints.go

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package graph
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import "github.com/TheAlgorithms/Go/math/min"
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type apHelper struct {
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is_ap []bool
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visited []bool
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child_cnt []int
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discovery_time []int
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earliest_discovery []int
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}
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// ArticulationPoint is a function to identify articulation points in a graph.
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// The function takes the graph as an argument and returns a boolean slice
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// which indicates whether a vertex is an articulation point or not.
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// Worst Case Time Complexity: O(|V| + |E|)
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// Auxiliary Space: O(|V|)
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// reference: https://en.wikipedia.org/wiki/Biconnected_component and https://cptalks.quora.com/Cut-Vertex-Articulation-point
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func ArticulationPoint(graph *Graph) []bool {
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// time variable to keep track of the time of discovery_time of a vertex
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time := 0
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//initialize all the variables
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apHelperInstance := &apHelper{
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is_ap: make([]bool, graph.vertices),
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visited: make([]bool, graph.vertices),
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child_cnt: make([]int, graph.vertices),
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// integer slice to store the discovery time of a vertex as we traverse
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// the graph in a depth first manner
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discovery_time: make([]int, graph.vertices),
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// integer slice to store the earliest discovered vertex reachable from a vertex
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earliest_discovery: make([]int, graph.vertices),
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}
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articulationPointHelper(
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apHelperInstance,
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0,
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-1,
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&time,
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graph,
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)
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if apHelperInstance.child_cnt[0] == 1 {
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// if the root has only one child, it is not an articulation point
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apHelperInstance.is_ap[0] = false
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}
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return apHelperInstance.is_ap
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}
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// articulationPointHelper is a recursive function to traverse the graph
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// and mark articulation points. Based on the depth first search transversal
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// of the graph, however modified to keep track and update the
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// `child_cnt`, `discovery_time`` and `earliest_discovery` slices defined above
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func articulationPointHelper(
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apHelperInstance *apHelper,
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vertex int,
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parent int,
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time *int,
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graph *Graph,
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) {
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apHelperInstance.visited[vertex] = true
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// Mark the time of discovery of a vertex
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// set the earliest discovery time to the discovered time
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// increment the time
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apHelperInstance.discovery_time[vertex] = *time
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apHelperInstance.earliest_discovery[vertex] = apHelperInstance.discovery_time[vertex]
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*time++
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for next_vertex := range graph.edges[vertex] {
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if next_vertex == parent {
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continue
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}
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if apHelperInstance.visited[next_vertex] {
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apHelperInstance.earliest_discovery[vertex] = min.Int(
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apHelperInstance.earliest_discovery[vertex],
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apHelperInstance.discovery_time[next_vertex],
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)
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continue
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}
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apHelperInstance.child_cnt[vertex]++
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articulationPointHelper(
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apHelperInstance,
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next_vertex,
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vertex,
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time,
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graph,
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)
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apHelperInstance.earliest_discovery[vertex] = min.Int(
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apHelperInstance.earliest_discovery[vertex],
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apHelperInstance.earliest_discovery[next_vertex],
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)
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if apHelperInstance.earliest_discovery[next_vertex] >= apHelperInstance.discovery_time[vertex] {
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apHelperInstance.is_ap[vertex] = true
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}
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}
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}

‎graph/articulationpoints_test.go

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package graph
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import (
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"reflect"
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"testing"
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)
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func TestArticulationPoints(t *testing.T) {
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var testCases = []struct {
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description string
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graph Graph
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expected []bool
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}{
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{
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"Linear tree structure",
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Graph{
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vertices: 5,
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edges: map[int]map[int]int{
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0: {
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1: 0,
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},
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1: {
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0: 0,
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2: 0,
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},
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2: {
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1: 0,
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3: 0,
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},
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3: {
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2: 0,
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4: 0,
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},
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},
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},
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[]bool{false, true, true, true, false},
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}, {
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"A complete graph",
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Graph{
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vertices: 4,
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edges: map[int]map[int]int{
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0: {
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1: 0,
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2: 0,
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3: 0,
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},
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1: {
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0: 0,
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2: 0,
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3: 0,
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},
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2: {
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0: 0,
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1: 0,
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3: 0,
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},
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3: {
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0: 0,
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1: 0,
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2: 0,
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},
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},
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},
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[]bool{false, false, false, false},
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},
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}
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for _, test := range testCases {
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t.Run(test.description, func(t *testing.T) {
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is_ap := ArticulationPoint(&test.graph)
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if !reflect.DeepEqual(is_ap, test.expected) {
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t.Logf("FAIL: %s", test.description)
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}
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})
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}
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}

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