Add Levenshtein Distance algorithm implementation

dynamic_programming/Levenshtein_Distance.R

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+# Levenshtein Distance Algorithm
+#
+# The Levenshtein distance measures the difference between two strings by
+# counting the minimum number of single-character edits required to
+# change one string into the other.
+#
+# Time Complexity: O(m * n) where m, n are the lengths of the strings
+# Space Complexity: O(m * n) for the DP table
+#
+# Applications:
+# - Spell checkers and auto-correct
+# - Fuzzy string searching in databases
+# - DNA sequence analysis in bioinformatics
+# - Plagiarism and duplicate content detection
+# - Optical Character Recognition (OCR) correction
+
+levenshtein_distance <- function(s1, s2) {
+  #' Calculate the Levenshtein distance between two strings
+  #' @param s1: First string
+  #' @param s2: Second string
+  #' @return: The integer Levenshtein distance
+
+  # Get the length of the strings
+  len1 <- nchar(s1)
+  len2 <- nchar(s2)
+
+  # Create a matrix to store the distances
+  dist_matrix <- matrix(0, nrow = len1 + 1, ncol = len2 + 1)
+
+  # Initialize the first row and column
+  # This represents the cost of transforming a prefix to an empty string
+  for (i in 1:(len1 + 1)) {
+    dist_matrix[i, 1] <- i - 1
+  }
+  for (j in 1:(len2 + 1)) {
+    dist_matrix[1, j] <- j - 1
+  }
+
+  # Fill the rest of the matrix
+  for (j in 2:(len2 + 1)) {
+    for (i in 2:(len1 + 1)) {
+      # Check if the characters at the current position are the same
+      # The cost of substitution is 0 if they are, 1 otherwise
+      substitution_cost <- if (substr(s1, i - 1, i - 1) == substr(s2, j - 1, j - 1)) 0 else 1
+
+      # Calculate the costs of insertion, deletion, and substitution
+      deletion <- dist_matrix[i - 1, j] + 1
+      insertion <- dist_matrix[i, j - 1] + 1
+      substitution <- dist_matrix[i - 1, j - 1] + substitution_cost
+
+      # The value of the current cell is the minimum of these three costs
+      dist_matrix[i, j] <- min(deletion, insertion, substitution)
+    }
+  }
+
+  # The final distance is in the bottom-right corner of the matrix
+  return(dist_matrix[len1 + 1, len2 + 1])
+}
+
+# Example usage and testing
+cat("=== Levenshtein Distance Algorithm ===\n\n")
+
+# Test 1: Classic example
+cat("1. Classic Example\n")
+str1 <- "saturday"
+str2 <- "sunday"
+cat("String 1:", str1, "\n")
+cat("String 2:", str2, "\n")
+cat("Distance:", levenshtein_distance(str1, str2), "\n\n")
+
+# Test 2: Another common example
+cat("2. Common Example\n")
+str1 <- "kitten"
+str2 <- "sitting"
+cat("String 1:", str1, "\n")
+cat("String 2:", str2, "\n")
+cat("Distance:", levenshtein_distance(str1, str2), "\n\n")
+
+# Test 3: Edge cases
+cat("3. Edge Cases\n")
+cat("Distance between 'apple' and '':", levenshtein_distance("apple", ""), "\n")
+cat("Distance between '' and 'banana':", levenshtein_distance("", "banana"), "\n")
+cat("Distance between 'book' and 'book':", levenshtein_distance("book", "book"), "\n")
+cat("Distance between 'car' and 'bus':", levenshtein_distance("car", "bus"), "\n\n")