Add Kosaraju's Strongly Connected Components algorithm (#256)

Brijesh03032001 · web-flow · commit 9954b50e5d4e · 2025-10-25T13:42:43.000+03:00
diff --git a/DIRECTORY.md b/DIRECTORY.md
@@ -57,6 +57,8 @@
   * [Depth First Search](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/depth_first_search.r)
   * [Dijkstra Shortest Path](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/dijkstra_shortest_path.r)
   * [Floyd Warshall](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/floyd_warshall.r)
+  * [Johnson Shortest Paths](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/johnson_shortest_paths.r)
+  * [Kosaraju Scc](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/kosaraju_scc.r)
 
 
 ## Linked List Algorithms
diff --git a/graph_algorithms/kosaraju_scc.r b/graph_algorithms/kosaraju_scc.r
@@ -0,0 +1,378 @@
+# Kosaraju's Algorithm for Finding Strongly Connected Components
+#
+# Kosaraju's algorithm is used to find all strongly connected components (SCCs) in a directed graph.
+# A strongly connected component is a maximal set of vertices such that there is a path from 
+# each vertex to every other vertex in the component.
+#
+# Algorithm Steps:
+# 1. Perform DFS on the original graph and store vertices in finishing order (stack)
+# 2. Create transpose graph (reverse all edge directions)
+# 3. Perform DFS on transpose graph in the order of decreasing finish times
+#
+# Time Complexity: O(V + E) where V is vertices and E is edges
+# Space Complexity: O(V) for visited arrays and recursion stack
+#
+# Author: Contributor for TheAlgorithms/R
+# Applications: Social network analysis, web crawling, circuit design verification
+
+# Helper function: DFS to fill stack with finishing times
+dfs_fill_order <- function(graph, vertex, visited, stack) {
+  # Mark current vertex as visited
+  visited[vertex] <- TRUE
+  
+  # Visit all adjacent vertices
+  if (as.character(vertex) %in% names(graph)) {
+    for (neighbor in graph[[as.character(vertex)]]) {
+      if (!visited[neighbor]) {
+        result <- dfs_fill_order(graph, neighbor, visited, stack)
+        stack <- result$stack
+        visited <- result$visited
+      }
+    }
+  }
+  
+  # Push current vertex to stack (finishing time)
+  stack <- c(stack, vertex)
+  
+  return(list(visited = visited, stack = stack))
+}
+
+# Helper function: DFS to collect vertices in current SCC
+dfs_collect_scc <- function(transpose_graph, vertex, visited, current_scc) {
+  # Mark current vertex as visited
+  visited[vertex] <- TRUE
+  current_scc <- c(current_scc, vertex)
+  
+  # Visit all adjacent vertices in transpose graph
+  if (as.character(vertex) %in% names(transpose_graph)) {
+    for (neighbor in transpose_graph[[as.character(vertex)]]) {
+      if (!visited[neighbor]) {
+        result <- dfs_collect_scc(transpose_graph, neighbor, visited, current_scc)
+        visited <- result$visited
+        current_scc <- result$current_scc
+      }
+    }
+  }
+  
+  return(list(visited = visited, current_scc = current_scc))
+}
+
+# Function to create transpose graph (reverse all edges)
+create_transpose_graph <- function(graph) {
+  # Initialize empty transpose graph
+  transpose_graph <- list()
+  
+  # Get all vertices
+  all_vertices <- unique(c(names(graph), unlist(graph)))
+  
+  # Initialize empty adjacency lists for all vertices
+  for (vertex in all_vertices) {
+    transpose_graph[[as.character(vertex)]] <- c()
+  }
+  
+  # Reverse all edges
+  for (vertex in names(graph)) {
+    for (neighbor in graph[[vertex]]) {
+      # Add edge from neighbor to vertex (reverse direction)
+      transpose_graph[[as.character(neighbor)]] <- 
+        c(transpose_graph[[as.character(neighbor)]], as.numeric(vertex))
+    }
+  }
+  
+  # Remove empty adjacency lists
+  transpose_graph <- transpose_graph[lengths(transpose_graph) > 0 | names(transpose_graph) %in% names(graph)]
+  
+  return(transpose_graph)
+}
+
+# Main Kosaraju's Algorithm function
+kosaraju_scc <- function(graph) {
+  #' Kosaraju's Algorithm for Strongly Connected Components
+  #' 
+  #' @param graph A named list representing adjacency list of directed graph
+  #'              Format: list("1" = c(2, 3), "2" = c(3), "3" = c())
+  #'              Keys are vertex names (as strings), values are vectors of adjacent vertices
+  #' 
+  #' @return A list containing:
+  #'   - scc_list: List of strongly connected components (each is a vector of vertices)
+  #'   - scc_count: Number of strongly connected components
+  #'   - vertex_to_scc: Named vector mapping each vertex to its SCC number
+  #'   - transpose_graph: The transpose graph used in algorithm
+  
+  # Input validation
+  if (!is.list(graph)) {
+    stop("Graph must be a list representing adjacency list")
+  }
+  
+  if (length(graph) == 0) {
+    return(list(scc_list = list(), scc_count = 0, vertex_to_scc = c(), transpose_graph = list()))
+  }
+  
+  # Get all vertices in the graph
+  all_vertices <- unique(c(names(graph), unlist(graph)))
+  max_vertex <- max(all_vertices)
+  
+  # Initialize visited array for first DFS
+  visited <- rep(FALSE, max_vertex)
+  names(visited) <- 1:max_vertex
+  stack <- c()
+  
+  # Step 1: Fill vertices in stack according to their finishing times
+  cat("Step 1: Performing DFS to determine finishing order...\n")
+  for (vertex in all_vertices) {
+    if (!visited[vertex]) {
+      result <- dfs_fill_order(graph, vertex, visited, stack)
+      visited <- result$visited
+      stack <- result$stack
+    }
+  }
+  
+  cat("Finishing order (stack):", rev(stack), "\n")
+  
+  # Step 2: Create transpose graph
+  cat("Step 2: Creating transpose graph...\n")
+  transpose_graph <- create_transpose_graph(graph)
+  
+  # Step 3: Perform DFS on transpose graph in order of decreasing finish times
+  cat("Step 3: Finding SCCs in transpose graph...\n")
+  visited <- rep(FALSE, max_vertex)
+  names(visited) <- 1:max_vertex
+  
+  scc_list <- list()
+  scc_count <- 0
+  vertex_to_scc <- rep(NA, max_vertex)
+  names(vertex_to_scc) <- 1:max_vertex
+  
+  # Process vertices in reverse finishing order
+  for (vertex in rev(stack)) {
+    if (!visited[vertex]) {
+      scc_count <- scc_count + 1
+      result <- dfs_collect_scc(transpose_graph, vertex, visited, c())
+      visited <- result$visited
+      current_scc <- sort(result$current_scc)
+      
+      scc_list[[scc_count]] <- current_scc
+      
+      # Map vertices to their SCC number
+      for (v in current_scc) {
+        vertex_to_scc[v] <- scc_count
+      }
+      
+      cat("SCC", scc_count, ":", current_scc, "\n")
+    }
+  }
+  
+  # Filter vertex_to_scc to only include vertices that exist in graph
+  vertex_to_scc <- vertex_to_scc[all_vertices]
+  
+  return(list(
+    scc_list = scc_list,
+    scc_count = scc_count,
+    vertex_to_scc = vertex_to_scc,
+    transpose_graph = transpose_graph
+  ))
+}
+
+# Print function for SCC results
+print_scc_results <- function(result) {
+  cat("\n=== KOSARAJU'S ALGORITHM RESULTS ===\n")
+  cat("Number of Strongly Connected Components:", result$scc_count, "\n\n")
+  
+  for (i in 1:result$scc_count) {
+    cat("SCC", i, ":", result$scc_list[[i]], "\n")
+  }
+  
+  cat("\nVertex to SCC mapping:\n")
+  for (vertex in names(result$vertex_to_scc)) {
+    if (!is.na(result$vertex_to_scc[vertex])) {
+      cat("Vertex", vertex, "-> SCC", result$vertex_to_scc[vertex], "\n")
+    }
+  }
+}
+
+# Function to visualize graph structure (text-based)
+print_graph <- function(graph, title = "Graph") {
+  cat("\n=== ", title, " ===\n")
+  if (length(graph) == 0) {
+    cat("Empty graph\n")
+    return()
+  }
+  
+  for (vertex in names(graph)) {
+    if (length(graph[[vertex]]) > 0) {
+      cat("Vertex", vertex, "->", graph[[vertex]], "\n")
+    } else {
+      cat("Vertex", vertex, "-> (no outgoing edges)\n")
+    }
+  }
+  
+  # Also show vertices with no outgoing edges
+  all_vertices <- unique(c(names(graph), unlist(graph)))
+  vertices_with_no_outgoing <- setdiff(all_vertices, names(graph))
+  for (vertex in vertices_with_no_outgoing) {
+    cat("Vertex", vertex, "-> (no outgoing edges)\n")
+  }
+}
+
+# ==============================================================================
+# EXAMPLES AND TEST CASES
+# ==============================================================================
+
+run_kosaraju_examples <- function() {
+  cat("=================================================================\n")
+  cat("KOSARAJU'S ALGORITHM - STRONGLY CONNECTED COMPONENTS EXAMPLES\n")
+  cat("=================================================================\n\n")
+  
+  # Example 1: Simple graph with 2 SCCs
+  cat("EXAMPLE 1: Simple Directed Graph with 2 SCCs\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  # Graph: 1 -> 2 -> 3 -> 1 (SCC: {1,2,3}) and 4 -> 5, 5 -> 4 (SCC: {4,5})
+  #        Also: 2 -> 4 (bridge between SCCs)
+  graph1 <- list(
+    "1" = c(2),
+    "2" = c(3, 4),
+    "3" = c(1),
+    "4" = c(5),
+    "5" = c(4)
+  )
+  
+  print_graph(graph1, "Example 1 - Original Graph")
+  result1 <- kosaraju_scc(graph1)
+  print_scc_results(result1)
+  
+  cat("\n=================================================================\n")
+  cat("EXAMPLE 2: Linear Chain (No Cycles)\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  # Graph: 1 -> 2 -> 3 -> 4 (Each vertex is its own SCC)
+  graph2 <- list(
+    "1" = c(2),
+    "2" = c(3),
+    "3" = c(4),
+    "4" = c()
+  )
+  
+  print_graph(graph2, "Example 2 - Linear Chain")
+  result2 <- kosaraju_scc(graph2)
+  print_scc_results(result2)
+  
+  cat("\n=================================================================\n")
+  cat("EXAMPLE 3: Complex Graph with Multiple SCCs\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  # More complex graph with 3 SCCs
+  # SCC 1: {1, 2, 3}  SCC 2: {4, 5, 6}  SCC 3: {7}
+  graph3 <- list(
+    "1" = c(2),
+    "2" = c(3, 4),
+    "3" = c(1),
+    "4" = c(5),
+    "5" = c(6),
+    "6" = c(4, 7),
+    "7" = c()
+  )
+  
+  print_graph(graph3, "Example 3 - Complex Graph")
+  result3 <- kosaraju_scc(graph3)
+  print_scc_results(result3)
+  
+  cat("\n=================================================================\n")
+  cat("EXAMPLE 4: Single Strongly Connected Component\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  # Complete cycle: 1 -> 2 -> 3 -> 4 -> 1
+  graph4 <- list(
+    "1" = c(2),
+    "2" = c(3),
+    "3" = c(4),
+    "4" = c(1)
+  )
+  
+  print_graph(graph4, "Example 4 - Single SCC")
+  result4 <- kosaraju_scc(graph4)
+  print_scc_results(result4)
+  
+  cat("\n=================================================================\n")
+  cat("EXAMPLE 5: Disconnected Graph\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  # Two separate components: {1 -> 2 -> 1} and {3 -> 4 -> 3}
+  graph5 <- list(
+    "1" = c(2),
+    "2" = c(1),
+    "3" = c(4),
+    "4" = c(3)
+  )
+  
+  print_graph(graph5, "Example 5 - Disconnected Graph")
+  result5 <- kosaraju_scc(graph5)
+  print_scc_results(result5)
+  
+  cat("\n=================================================================\n")
+  cat("PRACTICAL APPLICATION: Social Network Analysis\n")
+  cat("-----------------------------------------------------------------\n")
+  
+  cat("In social networks, SCCs represent groups of people who can\n")
+  cat("all reach each other through mutual connections. This is useful for:\n")
+  cat("- Community detection\n")
+  cat("- Information spread analysis\n") 
+  cat("- Influence maximization\n")
+  cat("- Network segmentation\n\n")
+  
+  # Example social network (simplified)
+  social_network <- list(
+    "Alice" = c("Bob"),
+    "Bob" = c("Charlie", "David"),
+    "Charlie" = c("Alice"),  # Forms cycle Alice->Bob->Charlie->Alice
+    "David" = c("Eve"),
+    "Eve" = c("David"),      # Forms cycle David->Eve->David
+    "Frank" = c()            # Isolated node
+  )
+  
+  cat("Social Network Example:\n")
+  print_graph(social_network, "Social Network Graph")
+  
+  # Note: This will work but vertex names will be converted to numbers
+  cat("Note: Algorithm works with numeric vertices. For named vertices,\n")
+  cat("you would need to create a mapping between names and numbers.\n\n")
+  
+  cat("=================================================================\n")
+  cat("END OF EXAMPLES\n")
+  cat("=================================================================\n")
+}
+
+# Utility function to convert named graph to numeric
+convert_named_to_numeric_graph <- function(named_graph) {
+  # Get unique vertex names
+  all_names <- unique(c(names(named_graph), unlist(named_graph)))
+  
+  # Create name to number mapping
+  name_to_num <- setNames(seq_along(all_names), all_names)
+  num_to_name <- setNames(all_names, seq_along(all_names))
+  
+  # Convert graph
+  numeric_graph <- list()
+  for (vertex_name in names(named_graph)) {
+    vertex_num <- name_to_num[vertex_name]
+    neighbors <- named_graph[[vertex_name]]
+    numeric_neighbors <- name_to_num[neighbors]
+    numeric_graph[[as.character(vertex_num)]] <- numeric_neighbors
+  }
+  
+  return(list(
+    graph = numeric_graph,
+    name_to_num = name_to_num,
+    num_to_name = num_to_name
+  ))
+}
+
+# Examples are available but not run automatically to avoid side effects
+# To run examples, execute: run_kosaraju_examples()
+if (interactive()) {
+  cat("Loading Kosaraju's Strongly Connected Components Algorithm...\n")
+  cat("Run 'run_kosaraju_examples()' to see examples and test cases.\n")
+}
+
+# Uncomment the following line to run examples automatically:
+# run_kosaraju_examples()
