Swift – Calculate Levenshtein distance

Ciao,

here a conversion on an old tutorial in Swift about the Levenshtein distance of two strings.

In information theory, linguistics and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after the Soviet mathematician Vladimir Levenshtein, who considered this distance in 1965.^[1]

Levenshtein distance may also be referred to as edit distance, although that term may also denote a larger family of distance metrics.^[2]:32 It is closely related to pairwise string alignments.

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I’ve implemented the “Iterative full matrix” algorithm.

First of all create a Array2d class:

class Array2D {
    var cols:Int, rows:Int
    var matrix: [Int]

    init(cols:Int, rows:Int) {
        self.cols = cols
        self.rows = rows
        matrix = Array(repeating: 0, count: cols * rows)
    }

    subscript(col:Int, row:Int) -> Int {
        get { return matrix[cols * row + col] }
        set { matrix[cols*row+col] = newValue }
    }

    func colCount() -> Int { return self.cols }
    func rowCount() -> Int { return self.rows }
}

Next thing is a custom min function used to reduce the values:

func min(_ numbers: Int...) -> Int {
    return numbers.reduce(numbers[0], {$0 < $1 ? $0 : $1})
}

and last one the core function to get your distance:

class func levenshteinDistance(aStr: String, bStr: String) -> Int {
    let a = Array(aStr.utf16)
    let b = Array(bStr.utf16)

    if a.count == 0 || b.count == 0 { return 100 }

    let dist = Array2D(cols: a.count + 1, rows: b.count + 1)
      
    for i in 1...a.count {
        dist[i, 0] = i
    }

    for j in 1...b.count {
        dist[0, j] = j
    }

    for i in 1...a.count {
        for j in 1...b.count {
            if a[i-1] == b[j-1] {
                dist[i, j] = dist[i-1, j-1]  // noop
            } else {
                dist[i, j] = StringUtils.min(
                    dist[i-1, j  ] + 1,  // deletion
                    dist[i,   j-1] + 1,  // insertion
                    dist[i-1, j-1] + 1   // substitution
                )
            }
        }
    }   

    return dist[a.count, b.count]
}

Now you can use in your projects!

if levenshteinDistance(aStr: "milano", bStr: "milao") < 3 {
  // do something
}

Note about the min function:

Remember to use the “YourClass.min()” instead of the classic “min” that in reality is the “Swift.min()” function. And do something different.

thanks!