Improving edit distance string extension

Sources/ArgumentParser/Utilities/StringExtensions.swift

@@ -141,30 +141,86 @@ extension StringProtocol where SubSequence == Substring {
       return Swift.max(rows, columns)
     }
 
-    var matrix = Array(repeating: Array(repeating: 0, count: columns + 1), count: rows + 1)
-
-    for row in 1...rows {
-      matrix[row][0] = row
+    // Trim common prefix and suffix
+    var selfStartTrim = self.startIndex
+    var targetStartTrim = target.startIndex
+    while selfStartTrim < self.endIndex &&
+          targetStartTrim < target.endIndex &&
+            self[selfStartTrim] == target[targetStartTrim] {
+      self.formIndex(after: &selfStartTrim)
+      target.formIndex(after: &targetStartTrim)
+    }
+
+    var selfEndTrim = self.endIndex
+    var targetEndTrim = target.endIndex
+
+    while selfEndTrim > selfStartTrim &&
+          targetEndTrim > targetStartTrim {
+      let selfIdx = self.index(before: selfEndTrim)
+      let targetIdx = target.index(before: targetEndTrim)
+
+      guard self[selfIdx] == target[targetIdx] else {
+        break
+      }
+
+      selfEndTrim = selfIdx
+      targetEndTrim = targetIdx
     }
-    for column in 1...columns {
-      matrix[0][column] = column
+
+    // Equal strings
+    guard !(selfStartTrim == self.endIndex &&
+          targetStartTrim == target.endIndex) else {
+      return 0
     }
 
-    for row in 1...rows {
-      for column in 1...columns {
-        let source = self[self.index(self.startIndex, offsetBy: row - 1)]
-        let target = target[target.index(target.startIndex, offsetBy: column - 1)]
-        let cost = source == target ? 0 : 1
-
-        matrix[row][column] = Swift.min(
-          matrix[row - 1][column] + 1,
-          matrix[row][column - 1] + 1,
-          matrix[row - 1][column - 1] + cost
-        )
+    // After trimming common prefix and suffix, self is empty.
+    guard selfStartTrim < selfEndTrim else {
+      return target.distance(from: targetStartTrim,
+                             to: targetEndTrim)
+    }
+
+    // After trimming common prefix and suffix, target is empty.
+    guard targetStartTrim < targetEndTrim else {
+      return distance(from: selfStartTrim,
+                      to: selfEndTrim)
+    }
+
+    let newSelf = self[selfStartTrim..<selfEndTrim]
+    let newTarget = target[targetStartTrim..<targetEndTrim]
+
+    let m = newSelf.count
+    let n = newTarget.count
+
+    // Initialize the levenshtein matrix with only two rows
+    // current and previous.
+    var previousRow = [Int](repeating: 0, count: n + 1)
+    var currentRow = [Int](0...n)
+
+    var sourceIdx = newSelf.startIndex
+    for i in 1...m {
+      swap(&previousRow, &currentRow)
+      currentRow[0] = i
+
+      var targetIdx = newTarget.startIndex
+      for j in 1...n {
+        // If characteres are equal for the levenshtein algorithm the
+        // minimum will always be the substitution cost, so we can fast
+        // path here in order to avoid min calls.
+        if newSelf[sourceIdx] == newTarget[targetIdx] {
+          currentRow[j] = previousRow[j - 1]
+        } else {
+          let deletion = previousRow[j]
+          let insertion = currentRow[j - 1]
+          let substitution = previousRow[j - 1]
+          currentRow[j] = Swift.min(deletion, Swift.min(insertion, substitution)) + 1
+        }
+        // j += 1
+        newTarget.formIndex(after: &targetIdx)
       }
+      // i += 1
+      newSelf.formIndex(after: &sourceIdx)
     }
-
-    return matrix.last!.last!
+    return currentRow[n]
   }
 
   func indentingEachLine(by n: Int) -> String {

Tests/ArgumentParserUnitTests/StringEditDistanceTests.swift

@@ -23,5 +23,10 @@ extension StringEditDistanceTests {
     XCTAssertEqual("bar".editDistance(to: "foo"), 3)
     XCTAssertEqual("bar".editDistance(to: "baz"), 1)
     XCTAssertEqual("baz".editDistance(to: "bar"), 1)
+    XCTAssertEqual("friend".editDistance(to: "fresh"), 3)
+    XCTAssertEqual("friend".editDistance(to: "friend"), 0)
+    XCTAssertEqual("friend".editDistance(to: "fried"), 1)
+    XCTAssertEqual("friend".editDistance(to: "friendly"), 2)
+    XCTAssertEqual("friendly".editDistance(to: "friend"), 2)
   }
 }