Project: s41467-024-52027-9 | Function: dfs (r)

system: You are an expert R programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow R best practices and maintain consistent code style.
Return **only** the complete R function code.

user: Complete this R function:

**DESCRIPTION:** Implements depth-first search algorithm to explore possible structural variation pathways and reconstruct series of mutations leading to observed genomic configurations

**KEY TERMS:** {
  "dfs": "depth-first search",
  "maxdepth": "maximum search depth",
  "earlystop": "early stopping criterion"
}

**CONTEXT CODE:** #' DFS caller function
#'
#' This function serves as the gateway to entering the DFS process. It calls the dfsutil function recursively
#' to explore possible paths within the search space.
#'
#' @param bitlocus A matrix representing the search space.
#' @param maxdepth The maximum depth of the search tree.
#' @param increase_only A boolean indicating whether only increasing mutations are allowed.
#' @param earlystop The maximum number of evaluations before the search is terminated.
#' @param history An optional argument representing previous search history.
#'
#' @return A list containing the search history and the evaluation results.
#'
#' @export
#' @author Wolfram Hoeps
#' @import digest
#' @import dplyr

dfs.R:
```r
#' DFS caller function
#'
#' This function serves as the gateway to entering the DFS process. It calls the dfsutil function recursively
#' to explore possible paths within the search space.
#'
#' @param bitlocus A matrix representing the search space.
#' @param maxdepth The maximum depth of the search tree.
#' @param increase_only A boolean indicating whether only increasing mutations are allowed.
#' @param earlystop The maximum number of evaluations before the search is terminated.
#' @param history An optional argument representing previous search history.
#'
#' @return A list containing the search history and the evaluation results.
#'
#' @export
#' @author Wolfram Hoeps
#' DFS caller function
#'
#' This function serves as the gateway to entering the DFS process. It calls the dfsutil function recursively
#' to explore possible paths within the search space.
#'
#' @param bitlocus A matrix representing the search space.
#' @param maxdepth The maximum depth of the search tree.
#' @param increase_only A boolean indicating whether only increasing mutations are allowed.
#' @param earlystop The maximum number of evaluations before the search is terminated.
#' @param history An optional argument representing previous search history.
#'
#' @return A list containing the search history and the evaluation results.
#'
#' @export
#' @author Wolfram Hoeps
dfs <- function(bitlocus, maxdepth = 3, increase_only = FALSE, earlystop = Inf, history = NULL) {
  stop("Function implementation has been masked")
}

#' DFS workhorse function
#'
#' This function recursively explores possible paths within the search space and returns a list containing
#' the search history and the evaluation results.
#'
#' @param visited A hash table containing the visited nodes.
#' @param pair A data frame representing a pair of points to be mutated.
#' @param pairhash A hash value representing the mutated pair.
#' @param mutator A matrix representing the mutated search space.
#' @param depth The current depth of the search tree.
#' @param maxdepth The maximum depth of the search tree.
#' @param pairhistory The search history up to the current pair.
#' @param df_output A data frame representing the evaluation results.
#' @param increase_only A boolean indicating whether only increasing mutations are allowed.
#' @param orig_symm The original symmetry value of the search space.
#' @param last_eval The score of the previous evaluation.
#' @param earlystop The maximum number of evaluations before the search is terminated.
#'
#' @return A list containing the search history and the evaluation results.
#'
#' @export
dfsutil <- function(visited, pair, pairhash, mutator, depth, maxdepth = 3, 
                    pairhistory = NULL, df_output = NULL, increase_only = NULL, 
                    orig_symm = 1, last_eval = 0, earlystop = Inf) {

  # Base case - max depth reached
  if (depth >= maxdepth) {
    return(list(history = pairhistory, results = df_output))
  }

  n <- nrow(mutator)
  m <- ncol(mutator)

  # Generate all possible pairs
  positions <- expand.grid(1:n, 1:m)
  colnames(positions) <- c("row", "col")
  pair_indices <- combn(nrow(positions), 2, simplify = FALSE)

  for (idx in pair_indices) {
    # Check early stopping condition
    if (!is.null(df_output) && nrow(df_output) >= earlystop) {
      return(list(history = pairhistory, results = df_output))
    }

    # Extract the current pair of coordinates
    loc1 <- positions[idx[1], , drop = FALSE]
    loc2 <- positions[idx[2], , drop = FALSE]

    # Skip if coordinates are the same
    if (identical(loc1, loc2)) next

    # Create new mutator by swapping locations
    new_mutator <- mutator
    temp <- new_mutator[loc1$row, loc1$col]
    new_mutator[loc1$row, loc1$col] <- new_mutator[loc2$row, loc2$col]
    new_mutator[loc2$row, loc2$col] <- temp

    # Generate hash for new state
    new_hash <- digest(new_mutator)

    # Check if new state is in visited
    if (exists(new_hash, visited)) next

    # Simple evaluation score (placeholder)
    current_score <- sum(new_mutator)

    # Enforce increase_only constraint
    if (increase_only && current_score <= last_eval) next

    # Add new state to visited tracking
    visited[[new_hash]] <- TRUE

    # Create pair record
    current_pair <- data.frame(
      i1 = loc1$row, j1 = loc1$col,
      i2 = loc2$row, j2 = loc2$col,
      stringsAsFactors = FALSE
    )

    # Update history
    new_history <- c(pairhistory, list(current_pair))

    # Update evaluation results
    new_entry <- data.frame(
      pair = list(current_pair),
      score = current_score,
      depth = depth + 1,
      stringsAsFactors = FALSE
    )
    new_df <- if (is.null(df_output)) new_entry else rbind(df_output, new_entry)

    # Recursive call
    recursive_result <- dfsutil(
      visited = visited,
      pair = current_pair,
      pairhash = new_hash,


Complete the function implementation replacing "stop("Not implemented")".