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Add Kosaraju Algorithm (#3859)

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Shivanagouda Agasimani
2023-02-08 23:35:52 +05:30
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commit 39df47b5f2
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src/main/java/com/thealgorithms/datastructures/graphs/Kosaraju.java Normal file
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package com.thealgorithms.datastructures.graphs;
import java.util.ArrayList;
import java.util.List;
import java.util.Stack;
/**
* Java program that implements Kosaraju Algorithm.
* @author Shivanagouda S A (https://github.com/shivu2002a)
*
*/
/**
* Kosaraju algorithm is a linear time algorithm to find the strongly connected components of a
directed graph, which, from here onwards will be referred by SCC. It leverages the fact that the transpose
graph (same graph with all the edges reversed) has exactly the same SCCs as the original graph.
* A graph is said to be strongly connected if every vertex is reachable from every other vertex.
The SCCs of a directed graph form a partition into subgraphs that are themselves strongly connected.
Single node is always a SCC.
* Example:
0 <--- 2 -------> 3 -------- > 4 ---- > 7
| ^ | ^ ^
| / | \ /
| / | \ /
v / v \ /
1 5 --> 6
For the above graph, the SCC list goes as follows:
0, 1, 2
3
4, 5, 6
7
We can also see that order of the nodes in an SCC doesn't matter since they are in cycle.
{@summary}
* Kosaraju Algorithm:
1. Perform DFS traversal of the graph. Push node to stack before returning. This gives edges sorted by lowest finish time.
2. Find the transpose graph by reversing the edges.
3. Pop nodes one by one from the stack and again to DFS on the modified graph.
The transpose graph of the above graph:
0 ---> 2 <------- 3 <------- 4 <------ 7
^ / ^ \ /
| / | \ /
| / | \ /
| v | v v
1 5 <--- 6
We can observe that this graph has the same SCC as that of original graph.
*/
public class Kosaraju {
// Sort edges according to lowest finish time
Stack<Integer> stack = new Stack<Integer>();
//Store each component
private List<Integer> scc = new ArrayList<>();
//All the strongly connected components
private List<List<Integer>> sccsList = new ArrayList<>();
/**
*
* @param v Node count
* @param list Adjacency list of graph
* @return List of SCCs
*/
public List<List<Integer>> kosaraju(int v, List<List<Integer>> list){
sortEdgesByLowestFinishTime(v, list);
List<List<Integer>> transposeGraph = createTransposeMatrix(v, list);
findStronglyConnectedComponents(v, transposeGraph);
return sccsList;
}
private void sortEdgesByLowestFinishTime(int v, List<List<Integer>> list){
int vis[] = new int[v];
for (int i = 0; i < v; i++) {
if(vis[i] == 0){
dfs(i, vis, list);
}
}
}
private List<List<Integer>> createTransposeMatrix(int v, List<List<Integer>> list) {
var transposeGraph = new ArrayList<List<Integer>>(v);
for (int i = 0; i < v; i++) {
transposeGraph.add(new ArrayList<>());
}
for (int i = 0; i < v; i++) {
for (Integer neigh : list.get(i)) {
transposeGraph.get(neigh).add(i);
}
}
return transposeGraph;
}
/**
*
* @param v Node count
* @param transposeGraph Transpose of the given adjacency list
*/
public void findStronglyConnectedComponents(int v, List<List<Integer>> transposeGraph){
int vis[] = new int[v];
while (!stack.isEmpty()) {
var node = stack.pop();
if(vis[node] == 0){
dfs2(node, vis, transposeGraph);
sccsList.add(scc);
scc = new ArrayList<>();
}
}
}
//Dfs to store the nodes in order of lowest finish time
private void dfs(int node, int vis[], List<List<Integer>> list){
vis[node] = 1;
for(Integer neighbour : list.get(node)){
if(vis[neighbour] == 0)
dfs(neighbour, vis, list);
}
stack.push(node);
}
//Dfs to find all the nodes of each strongly connected component
private void dfs2(int node, int vis[], List<List<Integer>> list){
vis[node] = 1;
for(Integer neighbour : list.get(node)){
if(vis[neighbour] == 0)
dfs2(neighbour, vis, list);
}
scc.add(node);
}
}

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src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java Normal file
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package com.thealgorithms.datastructures.graphs;
import static org.junit.jupiter.api.Assertions.assertTrue;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import org.junit.jupiter.api.Test;
public class KosarajuTest {
private Kosaraju kosaraju = new Kosaraju();
@Test
public void findStronglyConnectedComps() {
//Create a adjacency list of graph
var n = 8;
var adjList = new ArrayList<List<Integer>>(n);
for (int i = 0; i < n; i++) {
adjList.add(new ArrayList<>());
}
adjList.get(0).add(1);
adjList.get(1).add(2);
adjList.get(2).add(0);
adjList.get(2).add(3);
adjList.get(3).add(4);
adjList.get(4).add(5);
adjList.get(4).add(7);
adjList.get(5).add(6);
adjList.get(6).add(4);
adjList.get(6).add(7);
List<List<Integer>> actualResult = kosaraju.kosaraju(n, adjList);
List<List<Integer>> expectedResult = new ArrayList<>();
/*
Expected result:
0, 1, 2
3
5, 4, 6
7
*/
expectedResult.add(Arrays.asList(1, 2, 0));
expectedResult.add(Arrays.asList(3));
expectedResult.add(Arrays.asList(5, 6, 4));
expectedResult.add(Arrays.asList(7));
assertTrue(expectedResult.equals(actualResult));
}
@Test
public void findStronglyConnectedCompsShouldGetSingleNodes() {
//Create a adjacency list of graph
var n = 8;
var adjList = new ArrayList<List<Integer>>(n);
for (int i = 0; i < n; i++) {
adjList.add(new ArrayList<>());
}
adjList.get(0).add(1);
adjList.get(1).add(2);
adjList.get(2).add(3);
adjList.get(3).add(4);
adjList.get(4).add(5);
adjList.get(5).add(6);
adjList.get(6).add(7);
adjList.get(7).add(0);
List<List<Integer>> actualResult = kosaraju.kosaraju(n, adjList);
List<List<Integer>> expectedResult = new ArrayList<>();
/*
Expected result:
0, 1, 2, 3, 4, 5, 6, 7
*/
expectedResult.add(Arrays.asList(1, 2, 3, 4, 5, 6, 7, 0));
assertTrue(expectedResult.equals(actualResult));
}
}