feat: add Levenshtein edit distance algorithm

DIRECTORY.md

@@ -60,6 +60,7 @@
   * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/matrix_chain_multiplication.r)
   * [Minimum Path Sum](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/minimum_path_sum.r)
   * [Subset Sum](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/subset_sum.r)
+  * [Edit Distance (Levenshtein, Dynamic Programming)](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/edit_distance.r)
 
 ## Graph Algorithms
   * [Bellman Ford Shortest Path](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/bellman_ford_shortest_path.r)

documentation/edit_distance.md

@@ -0,0 +1,16 @@
+# Edit Distance
+
+Levenshtein edit distance calculates the minimum number of single-character insertions, deletions, and substitutions required to transform one string into another.
+
+``` r
+source("dynamic_programming/edit_distance.r")
+
+# Compute the edit distance
+distance <- edit_distance("kitten", "sitting")
+print(distance)
+
+# Reconstruct the optimal sequence of operations
+result <- edit_distance_with_path("kitten", "sitting")
+print(result$distance)
+print(result$operations)
+```

dynamic_programming/edit_distance.r

@@ -0,0 +1,105 @@
+# edit_distance.r
+# Levenshtein edit distance algorithm in R
+# Computes the minimum number of insertions, deletions, and substitutions
+# required to transform one string into another.
+# Time Complexity: O(m * n)
+# Space Complexity: O(m * n)
+
+# Compute the Levenshtein distance between two strings
+edit_distance <- function(str1, str2) {
+  #' @param str1: First string
+  #' @param str2: Second string
+  #' @return: Integer edit distance
+  if (!is.character(str1) || !is.character(str2)) {
+    stop("Both inputs must be character strings.")
+  }
+  if (length(str1) != 1 || length(str2) != 1) {
+    stop("Each input must be a single string.")
+  }
+
+  m <- nchar(str1)
+  n <- nchar(str2)
+  dp <- matrix(0L, nrow = m + 1, ncol = n + 1)
+
+  # base cases: transform empty prefix
+  dp[, 1] <- seq(0L, m)
+  dp[1, ] <- seq(0L, n)
+
+  for (i in seq_len(m) + 1L) {
+    for (j in seq_len(n) + 1L) {
+      cost <- if (substr(str1, i - 1, i - 1) == substr(str2, j - 1, j - 1)) 0L else 1L
+      dp[i, j] <- min(
+        dp[i - 1, j] + 1L,      # deletion
+        dp[i, j - 1] + 1L,      # insertion
+        dp[i - 1, j - 1] + cost # substitution
+      )
+    }
+  }
+
+  return(dp[m + 1, n + 1])
+}
+
+# Compute the edit distance and reconstruct an optimal alignment path
+edit_distance_with_path <- function(str1, str2) {
+  #' @param str1: First string
+  #' @param str2: Second string
+  #' @return: List with distance, operations, and dp table
+  if (!is.character(str1) || !is.character(str2)) {
+    stop("Both inputs must be character strings.")
+  }
+  if (length(str1) != 1 || length(str2) != 1) {
+    stop("Each input must be a single string.")
+  }
+
+  m <- nchar(str1)
+  n <- nchar(str2)
+  dp <- matrix(0L, nrow = m + 1, ncol = n + 1)
+  dp[, 1] <- seq(0L, m)
+  dp[1, ] <- seq(0L, n)
+
+  for (i in seq_len(m) + 1L) {
+    for (j in seq_len(n) + 1L) {
+      cost <- if (substr(str1, i - 1, i - 1) == substr(str2, j - 1, j - 1)) 0L else 1L
+      dp[i, j] <- min(
+        dp[i - 1, j] + 1L,
+        dp[i, j - 1] + 1L,
+        dp[i - 1, j - 1] + cost
+      )
+    }
+  }
+
+  i <- m + 1
+  j <- n + 1
+  ops <- character()
+
+  while (i > 1 || j > 1) {
+    if (i > 1 && j > 1 && dp[i, j] == dp[i - 1, j - 1] +
+        (substr(str1, i - 1, i - 1) != substr(str2, j - 1, j - 1))) {
+      if (substr(str1, i - 1, i - 1) == substr(str2, j - 1, j - 1)) {
+        ops <- c("match", ops)
+      } else {
+        ops <- c(sprintf("substitute '%s' -> '%s'", substr(str1, i - 1, i - 1), substr(str2, j - 1, j - 1)), ops)
+      }
+      i <- i - 1
+      j <- j - 1
+    } else if (i > 1 && dp[i, j] == dp[i - 1, j] + 1L) {
+      ops <- c(sprintf("delete '%s'", substr(str1, i - 1, i - 1)), ops)
+      i <- i - 1
+    } else {
+      ops <- c(sprintf("insert '%s'", substr(str2, j - 1, j - 1)), ops)
+      j <- j - 1
+    }
+  }
+
+  return(list(
+    distance = dp[m + 1, n + 1],
+    operations = ops,
+    dp_table = dp
+  ))
+}
+
+# Example usage:
+# print(edit_distance("kitten", "sitting"))
+# result <- edit_distance_with_path("kitten", "sitting")
+# print(result$distance)
+# print(result$operations)