feat : Add Iterative Deepening DFS)

graph_algorithms/iddfs.r

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+# Iterative Deepening Depth-First Search (IDDFS)
+#
+# IDDFS performs repeated depth-limited DFS from depth = 0..max_depth until a target
+# is found. It combines the optimality (in terms of shallowest solution) of BFS with
+# the space efficiency of DFS.
+#
+# Time Complexity: O(b^d) in the worst case, where b is branching factor and d depth
+# Space Complexity: O(d) recursion/stack depth
+
+# Formatting
+LINE_WIDTH <- 60
+
+print_line <- function(char = "-", width = LINE_WIDTH) {
+  cat(strrep(char, width), "\n", sep = "")
+}
+
+#' Normalize adjacency list graph
+#'
+#' Ensures graph is a named list with names "1".."N" where N is the maximum vertex id,
+#' and that all adjacency entries are integer vectors (possibly empty). Missing vertices
+#' are added with empty adjacency.
+#' @param graph A list mapping vertex id (character or numeric) to numeric neighbor vector
+#' @return A normalized adjacency list with names "1".."N"
+normalize_graph <- function(graph) {
+  if (!is.list(graph)) stop("graph must be a list")
+  # Collect vertices from names and neighbors
+  name_ids <- as.integer(names(graph))
+  if (any(is.na(name_ids))) {
+    bad_names <- names(graph)[is.na(name_ids)]
+    stop(
+      sprintf(
+        "graph names must be coercible to integers (e.g., '1','2',...). Problematic names: %s",
+        paste(bad_names, collapse = ", ")
+      )
+    )
+  }
+  neighbor_ids <- unlist(graph, use.names = FALSE)
+  if (length(neighbor_ids) == 0) neighbor_ids <- integer(0)
+  if (!is.integer(neighbor_ids)) neighbor_ids <- as.integer(neighbor_ids)
+  if (any(is.na(neighbor_ids))) stop("neighbors must be numeric/integer ids")
+  max_id <- max(c(0L, name_ids, neighbor_ids))
+  if (max_id < 1L) {
+    # empty graph
+    return(setNames(vector("list", 0L), character(0L)))
+  }
+  adj <- vector("list", max_id)
+  for (i in seq_len(max_id)) adj[[i]] <- integer(0)
+  # Fill from provided graph
+  for (i in seq_along(graph)) {
+    vid <- name_ids[i]
+    if (!length(graph[[i]])) {
+      adj[[vid]] <- integer(0)
+    } else {
+      nbrs <- as.integer(graph[[i]])
+      if (any(is.na(nbrs))) stop("neighbors must be numeric/integer ids")
+      # Filter out-of-range neighbors gracefully but warn
+      if (length(nbrs)) {
+        out_of_range <- nbrs < 1L
+        if (any(out_of_range)) {
+          warning("Removed neighbors < 1: ", paste(nbrs[out_of_range], collapse = ", "))
+          nbrs <- nbrs[!out_of_range]
+        }
+      }
+      adj[[vid]] <- nbrs
+    }
+  }
+  names(adj) <- as.character(seq_len(max_id))
+  adj
+}
+
+#' Depth-Limited Search (recursive)
+#'
+#' This version avoids global state and only prevents cycles along the current path.
+#' @param graph Normalized adjacency list from normalize_graph
+#' @param current Current vertex (integer)
+#' @param target Target vertex (integer)
+#' @param limit Remaining depth limit (integer >= 0)
+#' @param path Vector of vertices along the current path (for cycle avoidance)
+#' @return list(found=logical, path=integer vector when found)
+.depth_limited_search <- function(graph, current, target, limit, path) {
+  # Visit current
+  new_path <- c(path, current)
+  if (current == target) {
+    return(list(found = TRUE, path = new_path))
+  }
+  if (limit == 0L) {
+    return(list(found = FALSE, path = integer(0)))
+  }
+  # Explore neighbors
+  nbrs <- graph[[current]]
+  for (nbr in nbrs) {
+    # Avoid cycles within the current path
+    if (!(nbr %in% new_path)) {
+      res <- .depth_limited_search(graph, nbr, target, limit - 1L, new_path)
+      if (res$found) return(res)
+    }
+  }
+  return(list(found = FALSE, path = integer(0)))
+}
+
+#' Iterative Deepening DFS (IDDFS)
+#'
+#' @param graph A named list adjacency: names are vertices ("1","2",...), values are integer neighbors
+#' @param start Start vertex (integer)
+#' @param target Target vertex (integer)
+#' @param max_depth Maximum depth to search (integer >= 0)
+#' @param verbose If TRUE, prints progress; otherwise silent
+#' @return list(found=logical, depth=integer if found, path=integer vector when found)
+#' @examples
+#' g <- list("1"=c(2,3), "2"=c(4), "3"=c(5), "4"=c(), "5"=c())
+#' iddfs(g, start=1, target=5, max_depth=5, verbose=TRUE)
+iddfs <- function(graph, start, target, max_depth, verbose = TRUE) {
+  adj <- normalize_graph(graph)
+  if (!is.numeric(start) || !is.numeric(target)) {
+    stop("start and target must be numeric/integer")
+  }
+  start <- as.integer(start)
+  target <- as.integer(target)
+  if (length(adj) == 0L) return(list(found = FALSE, depth = NA_integer_, path = integer(0)))
+  n <- length(adj)
+  if (start < 1L || start > n || target < 1L || target > n) {
+    stop(sprintf("start and target must be in [1, %d]", n))
+  }
+  if (!is.numeric(max_depth) || max_depth < 0) stop("max_depth must be integer >= 0")
+  max_depth <- as.integer(max_depth)
+
+  if (verbose) {
+    cat("Iterative Deepening DFS\n")
+    print_line("=")
+  }
+
+  # Early exit if start is target
+  if (start == target) {
+    if (verbose) {
+      cat(sprintf("✓ Target %d found at depth 0\n", target))
+      print_line("-")
+    }
+    return(list(found = TRUE, depth = 0L, path = c(start)))
+  }
+
+  for (depth in 0:max_depth) {
+    if (verbose) cat(sprintf("Searching at depth limit: %d\n", depth))
+    res <- .depth_limited_search(adj, start, target, depth, integer(0))
+    if (res$found) {
+      if (verbose) {
+        cat(sprintf("✓ Target %d found at depth %d\n", target, depth))
+        print_line("-")
+      }
+      return(list(found = TRUE, depth = depth, path = res$path))
+    }
+  }
+
+  if (verbose) {
+    cat(sprintf("✗ Target %d not found up to depth %d\n", target, max_depth))
+    print_line("-")
+  }
+  return(list(found = FALSE, depth = NA_integer_, path = integer(0)))
+}
+
+#' Example demonstrations for IDDFS
+#' @return NULL (prints results)
+example_iddfs <- function() {
+  cat("\n========== Example 1: Simple Directed Graph ==========\n")
+  graph1 <- list(
+    "1" = c(2, 3),
+    "2" = c(4),
+    "3" = c(5),
+    "4" = c(),
+    "5" = c()
+  )
+  print(iddfs(graph1, start = 1, target = 5, max_depth = 5, verbose = TRUE))
+
+  cat("\n========== Example 2: Target Not Found ==========\n")
+  graph2 <- list(
+    "1" = c(2),
+    "2" = c(3),
+    "3" = c()
+  )
+  print(iddfs(graph2, start = 1, target = 6, max_depth = 3, verbose = TRUE))
+
+  cat("\n========== Example 3: Larger Graph ==========\n")
+  graph3 <- list(
+    "1" = c(2, 3, 4),
+    "2" = c(5, 6),
+    "3" = c(7),
+    "4" = c(8),
+    "5" = c(),
+    "6" = c(),
+    "7" = c(9),
+    "8" = c(),
+    "9" = c()
+  )
+  print(iddfs(graph3, start = 1, target = 9, max_depth = 5, verbose = TRUE))
+
+  invisible(NULL)
+}
+
+# Uncomment to run examples when sourcing this file interactively
+# if (interactive()) example_iddfs()