feat: add Levenshtein edit distance algorithm

[DiogoRibeiro7]

Description

• Adds dynamic_programming/edit_distance.r implementing:
  • edit_distance(str1, str2) for Levenshtein distance
  • edit_distance_with_path(str1, str2) to return distance plus one optimal operation sequence
• Adds user documentation at documentation/edit_distance.md with usage examples.
• Updates DIRECTORY.md to include Edit Distance under Dynamic Programming.

Validation

• Ran:
  • edit_distance("kitten", "sitting")
  • edit_distance_with_path("kitten", "sitting")
• Result:
  • Distance = 3
  • Path distance = 3

[Copilot]

Pull request overview

Adds a Levenshtein (edit distance) implementation to the R algorithms collection, with an optional backtracking routine to return one optimal edit-operation sequence, plus accompanying documentation and directory indexing.

Changes:

• Added dynamic_programming/edit_distance.r with edit_distance() and edit_distance_with_path().
• Added documentation/edit_distance.md with basic usage examples.
• Updated DIRECTORY.md to list the new Dynamic Programming entry.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 4 comments.

File	Description
dynamic_programming/edit_distance.r	Introduces Levenshtein distance DP implementation and path reconstruction output.
documentation/edit_distance.md	Adds user-facing usage snippet for the new functions.
DIRECTORY.md	Adds a new link entry for “Edit Distance” under Dynamic Programming.

[Copilot]

The loops for (i in 2:(m + 1)) / for (j in 2:(n + 1)) break for empty strings (e.g., m == 0 makes 2:(m+1) evaluate to c(2, 1)), which can index outside dp and error. Use an empty-safe iteration pattern (e.g., seq_len(m) + 1, seq_len(n) + 1) or early-return when m == 0 or n == 0.

Suggested change

	for (i in 2:(m + 1)) {
	for (j in 2:(n + 1)) {
	for (i in seq_len(m) + 1L) {
	for (j in seq_len(n) + 1L) {

[Copilot]

Same empty-string issue as above: for (i in 2:(m + 1)) / for (j in 2:(n + 1)) can iterate invalid indices when m == 0 or n == 0, leading to out-of-bounds dp access. Please make the iteration empty-safe or handle m == 0 / n == 0 up front (and still produce a valid operations list).

[Copilot]

This repository already contains a Levenshtein distance implementation (string_manipulation/levenshtein.r, also linked in DIRECTORY.md). Adding a second Levenshtein implementation under Dynamic Programming may be redundant/confusing for users; consider consolidating (extend the existing implementation to optionally return a path) or clearly differentiating this entry (e.g., mention that it returns an operation sequence).

Suggested change

	* [Edit Distance](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/edit_distance.r)
	* [Edit Distance (Levenshtein, Dynamic Programming)](https://github.com/TheAlgorithms/R/blob/HEAD/dynamic_programming/edit_distance.r)

[Copilot]

source("../dynamic_programming/edit_distance.r") depends on the working directory being documentation/. If a user runs this from the repo root (common), it will point outside the repository. Consider using a repo-root-relative path (e.g., dynamic_programming/edit_distance.r) or embedding the relevant function code in the doc, consistent with other docs in this folder.

Suggested change

	source("../dynamic_programming/edit_distance.r")
	source("dynamic_programming/edit_distance.r")

[siriak]

It's already implemented here

R/string_manipulation/levenshtein.r

Line 5 in 2349f54

levenshtein_distance <- function(s1, s2) {