bidirectional_bfs (#226)

Author: Prathameshk2024

graph_algorithms/bidirectional_bfs.r

@@ -0,0 +1,153 @@
+# ==============================================================
+# Bidirectional Breadth-First Search (BFS) Shortest Path Algorithm
+# ==============================================================
+#
+# Description:
+#   Finds the shortest path between a source and target in an
+#   unweighted graph using Bidirectional BFS.
+#
+# Time Complexity: O(b^(d/2)) — much faster than normal BFS O(b^d)
+# Space Complexity: O(V)
+#
+# Input:
+#   graph  - adjacency list (list of integer vectors)
+#   source - integer (starting vertex)
+#   target - integer (destination vertex)
+#
+# Output:
+#   A list containing:
+#       path       - vector of vertices representing the path
+#       distance   - number of edges in the shortest path
+#       found      - logical flag (TRUE if path found, else FALSE)
+#
+# Example usage at bottom of file.
+# ==============================================================
+
+bidirectional_bfs <- function(graph, source, target) {
+  if (source == target) {
+    return(list(path = c(source), distance = 0, found = TRUE))
+  }
+
+  # Initialize BFS from both ends
+  visited_from_source <- setNames(rep(FALSE, length(graph)), names(graph))
+  visited_from_target <- setNames(rep(FALSE, length(graph)), names(graph))
+  
+  parent_from_source <- rep(NA, length(graph))
+  parent_from_target <- rep(NA, length(graph))
+  
+  queue_source <- c(source)
+  queue_target <- c(target)
+  
+  visited_from_source[source] <- TRUE
+  visited_from_target[target] <- TRUE
+  
+  meeting_node <- NA
+  
+  # Function to check intersection
+  get_intersection <- function() {
+    common <- which(visited_from_source & visited_from_target)
+    if (length(common) > 0) return(common[1])
+    return(NA)
+  }
+  
+  # Main loop
+  while (length(queue_source) > 0 && length(queue_target) > 0) {
+    # Expand one level from source side
+    next_queue <- c()
+    for (u in queue_source) {
+      for (v in graph[[as.character(u)]]) {
+        if (!visited_from_source[v]) {
+          visited_from_source[v] <- TRUE
+          parent_from_source[v] <- u
+          next_queue <- c(next_queue, v)
+        }
+      }
+    }
+    queue_source <- next_queue
+    
+    # Check intersection
+    meeting_node <- get_intersection()
+    if (!is.na(meeting_node)) break
+    
+    # Expand one level from target side
+    next_queue <- c()
+    for (u in queue_target) {
+      for (v in graph[[as.character(u)]]) {
+        if (!visited_from_target[v]) {
+          visited_from_target[v] <- TRUE
+          parent_from_target[v] <- u
+          next_queue <- c(next_queue, v)
+        }
+      }
+    }
+    queue_target <- next_queue
+    
+    # Check intersection again
+    meeting_node <- get_intersection()
+    if (!is.na(meeting_node)) break
+  }
+  
+  if (is.na(meeting_node)) {
+    return(list(path = NULL, distance = Inf, found = FALSE))
+  }
+  
+  # Reconstruct path from source → meeting_node
+  path1 <- c()
+  node <- meeting_node
+  while (!is.na(node)) {
+    path1 <- c(node, path1)
+    node <- parent_from_source[node]
+  }
+  
+  # Reconstruct path from meeting_node → target
+  path2 <- c()
+  node <- parent_from_target[meeting_node]
+  while (!is.na(node)) {
+    path2 <- c(path2, node)
+    node <- parent_from_target[node]
+  }
+  
+  full_path <- c(path1, path2)
+  return(list(path = full_path, distance = length(full_path) - 1, found = TRUE))
+}
+
+# ==============================================================
+# Example Usage and Test
+# ==============================================================
+
+cat("=== Bidirectional BFS Shortest Path ===\n")
+
+# Example Graph (Unweighted)
+# 1 -- 2 -- 3
+#  |    |
+#  4 -- 5 -- 6
+
+graph <- list(
+  "1" = c(2, 4),
+  "2" = c(1, 3, 5),
+  "3" = c(2, 6),
+  "4" = c(1, 5),
+  "5" = c(2, 4, 6),
+  "6" = c(3, 5)
+)
+
+cat("Graph adjacency list:\n")
+for (v in names(graph)) {
+  cat("Vertex", v, "-> [", paste(graph[[v]], collapse = ", "), "]\n")
+}
+
+cat("\nRunning Bidirectional BFS from 1 to 6...\n")
+result <- bidirectional_bfs(graph, 1, 6)
+
+if (result$found) {
+  cat("Shortest Path Found!\n")
+  cat("Path:", paste(result$path, collapse = " -> "), "\n")
+  cat("Distance:", result$distance, "\n")
+} else {
+  cat("No path found between source and target.\n")
+}
+    return(list(
+        distances = distances,
+        predecessor = predecessor,
+        found = found
+    ))