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Enhance docs, add more tests in Kosaraju (#5966)
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‎src/main/java/com/thealgorithms/datastructures/graphs/Kosaraju.java

+90-65
Original file line numberDiff line numberDiff line change
@@ -5,82 +5,91 @@
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import java.util.Stack;
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/**
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* Java program that implements Kosaraju Algorithm.
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* @author <a href="https://github.com/shivu2002a">Shivanagouda S A</a>
8+
* This class implements the Kosaraju Algorithm to find all the Strongly Connected Components (SCCs)
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* of a directed graph. Kosaraju's algorithm runs in linear time and leverages the concept that
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* the SCCs of a directed graph remain the same in its transpose (reverse) graph.
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*
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* <p>
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* Kosaraju algorithm is a linear time algorithm to find the strongly connected components of a
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directed graph, which, from here onwards will be referred by SCC. It leverages the fact that the
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transpose graph (same graph with all the edges reversed) has exactly the same SCCs as the original
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graph.
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* A graph is said to be strongly connected if every vertex is reachable from every other vertex.
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The SCCs of a directed graph form a partition into subgraphs that are themselves strongly
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connected. Single node is always a SCC.
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* Example:
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0 <--- 2 -------> 3 -------- > 4 ---- > 7
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| ^ | ^ ^
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| / | \ /
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| / | \ /
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v / v \ /
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1 5 --> 6
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For the above graph, the SCC list goes as follows:
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0, 1, 2
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3
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4, 5, 6
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7
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We can also see that order of the nodes in an SCC doesn't matter since they are in cycle.
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{@summary}
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* Kosaraju Algorithm:
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1. Perform DFS traversal of the graph. Push node to stack before returning. This gives edges
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sorted by lowest finish time.
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2. Find the transpose graph by reversing the edges.
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3. Pop nodes one by one from the stack and again to DFS on the modified graph.
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The transpose graph of the above graph:
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0 ---> 2 <------- 3 <------- 4 <------ 7
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^ / ^ \ /
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| / | \ /
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| / | \ /
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| v | v v
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1 5 <--- 6
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We can observe that this graph has the same SCC as that of original graph.
53-
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* A strongly connected component (SCC) of a directed graph is a subgraph where every vertex
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* is reachable from every other vertex in the subgraph. The Kosaraju algorithm is particularly
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* efficient for finding SCCs because it performs two Depth First Search (DFS) passes on the
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* graph and its transpose.
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* </p>
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*
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* <p><strong>Algorithm:</strong></p>
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* <ol>
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* <li>Perform DFS on the original graph and push nodes to a stack in the order of their finishing time.</li>
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* <li>Generate the transpose (reversed edges) of the original graph.</li>
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* <li>Perform DFS on the transpose graph, using the stack from the first DFS. Each DFS run on the transpose graph gives a SCC.</li>
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* </ol>
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*
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* <p><strong>Example Graph:</strong></p>
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* <pre>
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* 0 <--- 2 -------> 3 -------- > 4 ---- > 7
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* | ^ | ^ ^
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* | / | \ /
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* | / | \ /
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* v / v \ /
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* 1 5 --> 6
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* </pre>
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*
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* <p><strong>SCCs in the example:</strong></p>
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* <ul>
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* <li>{0, 1, 2}</li>
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* <li>{3}</li>
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* <li>{4, 5, 6}</li>
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* <li>{7}</li>
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* </ul>
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*
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* <p>The order of nodes in an SCC does not matter because every node in an SCC is reachable from every other node within the same SCC.</p>
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*
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* <p><strong>Graph Transpose Example:</strong></p>
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* <pre>
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* 0 ---> 2 <------- 3 <------- 4 <------ 7
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* ^ / ^ \ /
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* | / | \ /
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* | / | \ /
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* | v | v v
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* 1 5 <--- 6
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* </pre>
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*
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* The SCCs of this transpose graph are the same as the original graph.
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*/
55-
5658
public class Kosaraju {
5759

58-
// Sort edges according to lowest finish time
59-
Stack<Integer> stack = new Stack<Integer>();
60+
// Stack to sort edges by the lowest finish time (used in the first DFS)
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private final Stack<Integer> stack = new Stack<>();
6062

61-
// Store each component
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// Store each strongly connected component
6264
private List<Integer> scc = new ArrayList<>();
6365

64-
// All the strongly connected components
65-
private List<List<Integer>> sccsList = new ArrayList<>();
66+
// List of all SCCs
67+
private final List<List<Integer>> sccsList = new ArrayList<>();
6668

6769
/**
70+
* Main function to perform Kosaraju's Algorithm.
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* Steps:
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* 1. Sort nodes by the lowest finishing time
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* 2. Create the transpose (reverse edges) of the original graph
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* 3. Find SCCs by performing DFS on the transpose graph
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* 4. Return the list of SCCs
6876
*
69-
* @param v Node count
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* @param list Adjacency list of graph
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* @return List of SCCs
77+
* @param v the number of vertices in the graph
78+
* @param list the adjacency list representing the directed graph
79+
* @return a list of SCCs where each SCC is a list of vertices
7280
*/
7381
public List<List<Integer>> kosaraju(int v, List<List<Integer>> list) {
74-
7582
sortEdgesByLowestFinishTime(v, list);
76-
7783
List<List<Integer>> transposeGraph = createTransposeMatrix(v, list);
78-
7984
findStronglyConnectedComponents(v, transposeGraph);
80-
8185
return sccsList;
8286
}
8387

88+
/**
89+
* Performs DFS on the original graph to sort nodes by their finishing times.
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* @param v the number of vertices in the graph
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* @param list the adjacency list representing the original graph
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*/
8493
private void sortEdgesByLowestFinishTime(int v, List<List<Integer>> list) {
8594
int[] vis = new int[v];
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for (int i = 0; i < v; i++) {
@@ -90,8 +99,14 @@ private void sortEdgesByLowestFinishTime(int v, List<List<Integer>> list) {
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}
91100
}
92101

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/**
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* Creates the transpose (reverse) of the original graph.
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* @param v the number of vertices in the graph
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* @param list the adjacency list representing the original graph
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* @return the adjacency list representing the transposed graph
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*/
93108
private List<List<Integer>> createTransposeMatrix(int v, List<List<Integer>> list) {
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var transposeGraph = new ArrayList<List<Integer>>(v);
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List<List<Integer>> transposeGraph = new ArrayList<>(v);
95110
for (int i = 0; i < v; i++) {
96111
transposeGraph.add(new ArrayList<>());
97112
}
@@ -104,14 +119,14 @@ private List<List<Integer>> createTransposeMatrix(int v, List<List<Integer>> lis
104119
}
105120

106121
/**
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*
108-
* @param v Node count
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* @param transposeGraph Transpose of the given adjacency list
122+
* Finds the strongly connected components (SCCs) by performing DFS on the transposed graph.
123+
* @param v the number of vertices in the graph
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* @param transposeGraph the adjacency list representing the transposed graph
110125
*/
111126
public void findStronglyConnectedComponents(int v, List<List<Integer>> transposeGraph) {
112127
int[] vis = new int[v];
113128
while (!stack.isEmpty()) {
114-
var node = stack.pop();
129+
int node = stack.pop();
115130
if (vis[node] == 0) {
116131
dfs2(node, vis, transposeGraph);
117132
sccsList.add(scc);
@@ -120,7 +135,12 @@ public void findStronglyConnectedComponents(int v, List<List<Integer>> transpose
120135
}
121136
}
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123-
// Dfs to store the nodes in order of lowest finish time
138+
/**
139+
* Performs DFS on the original graph and pushes nodes onto the stack in order of their finish time.
140+
* @param node the current node being visited
141+
* @param vis array to keep track of visited nodes
142+
* @param list the adjacency list of the graph
143+
*/
124144
private void dfs(int node, int[] vis, List<List<Integer>> list) {
125145
vis[node] = 1;
126146
for (Integer neighbour : list.get(node)) {
@@ -131,7 +151,12 @@ private void dfs(int node, int[] vis, List<List<Integer>> list) {
131151
stack.push(node);
132152
}
133153

134-
// Dfs to find all the nodes of each strongly connected component
154+
/**
155+
* Performs DFS on the transposed graph to find the strongly connected components.
156+
* @param node the current node being visited
157+
* @param vis array to keep track of visited nodes
158+
* @param list the adjacency list of the transposed graph
159+
*/
135160
private void dfs2(int node, int[] vis, List<List<Integer>> list) {
136161
vis[node] = 1;
137162
for (Integer neighbour : list.get(node)) {

‎src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java

+53-21
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@@ -1,6 +1,6 @@
11
package com.thealgorithms.datastructures.graphs;
22

3-
import static org.junit.jupiter.api.Assertions.assertTrue;
3+
import static org.junit.jupiter.api.Assertions.assertEquals;
44

55
import java.util.ArrayList;
66
import java.util.Arrays;
@@ -9,14 +9,13 @@
99

1010
public class KosarajuTest {
1111

12-
private Kosaraju kosaraju = new Kosaraju();
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private final Kosaraju kosaraju = new Kosaraju();
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1414
@Test
15-
public void findStronglyConnectedComps() {
16-
// Create a adjacency list of graph
17-
var n = 8;
18-
var adjList = new ArrayList<List<Integer>>(n);
19-
15+
public void testFindStronglyConnectedComponents() {
16+
// Create a graph using adjacency list
17+
int n = 8;
18+
List<List<Integer>> adjList = new ArrayList<>(n);
2019
for (int i = 0; i < n; i++) {
2120
adjList.add(new ArrayList<>());
2221
}
@@ -36,24 +35,24 @@ public void findStronglyConnectedComps() {
3635
List<List<Integer>> expectedResult = new ArrayList<>();
3736
/*
3837
Expected result:
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0, 1, 2
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3
41-
5, 4, 6
42-
7
38+
{0, 1, 2}
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{3}
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{5, 4, 6}
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{7}
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*/
4443
expectedResult.add(Arrays.asList(1, 2, 0));
45-
expectedResult.add(Arrays.asList(3));
44+
expectedResult.add(List.of(3));
4645
expectedResult.add(Arrays.asList(5, 6, 4));
47-
expectedResult.add(Arrays.asList(7));
48-
assertTrue(expectedResult.equals(actualResult));
46+
expectedResult.add(List.of(7));
47+
48+
assertEquals(expectedResult, actualResult);
4949
}
5050

5151
@Test
52-
public void findStronglyConnectedCompsShouldGetSingleNodes() {
53-
// Create a adjacency list of graph
54-
var n = 8;
55-
var adjList = new ArrayList<List<Integer>>(n);
56-
52+
public void testFindSingleNodeSCC() {
53+
// Create a simple graph using adjacency list
54+
int n = 8;
55+
List<List<Integer>> adjList = new ArrayList<>(n);
5756
for (int i = 0; i < n; i++) {
5857
adjList.add(new ArrayList<>());
5958
}
@@ -71,9 +70,42 @@ public void findStronglyConnectedCompsShouldGetSingleNodes() {
7170
List<List<Integer>> expectedResult = new ArrayList<>();
7271
/*
7372
Expected result:
74-
0, 1, 2, 3, 4, 5, 6, 7
73+
{0, 1, 2, 3, 4, 5, 6, 7}
7574
*/
7675
expectedResult.add(Arrays.asList(1, 2, 3, 4, 5, 6, 7, 0));
77-
assertTrue(expectedResult.equals(actualResult));
76+
77+
assertEquals(expectedResult, actualResult);
78+
}
79+
80+
@Test
81+
public void testDisconnectedGraph() {
82+
// Create a disconnected graph (two separate components)
83+
int n = 5;
84+
List<List<Integer>> adjList = new ArrayList<>(n);
85+
for (int i = 0; i < n; i++) {
86+
adjList.add(new ArrayList<>());
87+
}
88+
89+
// Add edges for first component
90+
adjList.get(0).add(1);
91+
adjList.get(1).add(2);
92+
adjList.get(2).add(0);
93+
94+
// Add edges for second component
95+
adjList.get(3).add(4);
96+
adjList.get(4).add(3);
97+
98+
List<List<Integer>> actualResult = kosaraju.kosaraju(n, adjList);
99+
100+
List<List<Integer>> expectedResult = new ArrayList<>();
101+
/*
102+
Expected result:
103+
{0, 1, 2}
104+
{3, 4}
105+
*/
106+
expectedResult.add(Arrays.asList(4, 3));
107+
expectedResult.add(Arrays.asList(1, 2, 0));
108+
109+
assertEquals(expectedResult, actualResult);
78110
}
79111
}

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