Das Ermitteln der Levenshtein-Distanz ist nur eine dieser Aufgaben, die einfach für die dynamische Programmierung ausgelegt sind. Die klassische Lösung besteht darin, eine Größenmatrix zu erstellen $$ (wo $$ und $$ - die Länge der Linien) und ihre zeilenweise Füllung von oben nach unten. Leider, wenn die Zeilen eine lächerliche Größe in der Größenordnung von zehn Kilobyte haben, dann verschlingt eine solche Matrix 0,5-1 Gigabyte, was nicht sehr schön ist. Wenn Sie genau hinschauen, werden Sie jedoch feststellen, dass wir zu jedem Zeitpunkt nur zwei Zeilen verwenden (die aktuelle zu füllende und die vorherige), daher können wir sie nur speichern.

In der Tat können Sie mit einer Leitung auskommen, aber es wird für uns mit zwei gut sein.

, L2-, L1 . ? , :

• 20000 : 40 ( , L1 !).
• 20000 8- , 160 — 320 ( 4- , 160 , L1).

/ L2?

20000 , (20 ), (160 ), ( 160 ). , ( ) : (20 + 160)×20000 L2, 3.6 . , , , Haswell L2 50 /, 0.1 , 0.2 . .

, , , , L1, .

C++:

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
#include <string>

size_t lev_dist(const std::string& s1, const std::string& s2)
{
  const auto m = s1.size();
  const auto n = s2.size();

  std::vector<int64_t> v0;
  v0.resize(n + 1);
  std::iota(v0.begin(), v0.end(), 0);

  auto v1 = v0;

  for (size_t i = 0; i < m; ++i)
  {
    v1[0] = i + 1;

    for (size_t j = 0; j < n; ++j)
    {
      auto delCost = v0[j + 1] + 1;
      auto insCost = v1[j] + 1;
      auto substCost = s1[i] == s2[j] ? v0[j] : (v0[j] + 1);

      v1[j + 1] = std::min({ delCost, insCost, substCost });
    }

    std::swap(v0, v1);
  }

  return v0[n];
}

int main()
{
    std::string s1(20000, 'a');
    std::string s2(20000, 'a');
    std::string s3(20000, 'b');

    std::cout << lev_dist(s1, s2) << std::endl;
    std::cout << lev_dist(s1, s3) << std::endl;
}

— 1.356 (Core i7 4770, ). gcc 9.2, — -O3 -march=native.

, clang (9.0.1, , ) : 2.6-2.7 .

import qualified Data.ByteString as BS
import qualified Data.ByteString.Unsafe as BS
import qualified Data.Vector.Unboxed as V
import Data.List

levenshteinDistance :: BS.ByteString -> BS.ByteString -> Int
levenshteinDistance s1 s2 = foldl' outer (V.generate (n + 1) id) [0 .. m - 1] V.! n
  where
    m = BS.length s1
    n = BS.length s2

    outer v0 i = V.constructN (n + 1) ctr
      where
        s1char = s1 `BS.unsafeIndex` i
        ctr v1 | V.length v1 == 0 = i + 1
        ctr v1 = min (substCost + substCostBase) $ 1 + min delCost insCost
          where
            j = V.length v1
            delCost = v0 `V.unsafeIndex` j
            insCost = v1 `V.unsafeIndex` (j - 1)
            substCostBase = v0 `V.unsafeIndex` (j - 1)
            substCost = if s1char == s2 `BS.unsafeIndex` (j - 1) then 0 else 1

{-# LANGUAGE Strict #-}
{-# OPTIONS_GHC -fllvm #-}

import qualified Data.Array.Base as A(unsafeRead, unsafeWrite)
import qualified Data.Array.ST as A
import qualified Data.ByteString as BS
import qualified Data.ByteString.Unsafe as BS
import Control.Monad.ST

levenshteinDistance :: BS.ByteString -> BS.ByteString -> Int
levenshteinDistance s1 s2 = runST $ do
  v0Init <- A.newListArray (0, n) [0..]
  v1Init <- A.newArray_ (0, n)
  loop 0 v0Init v1Init
  A.unsafeRead (if even m then v0Init else v1Init) n

  where
    m = BS.length s1
    n = BS.length s2

    loop :: Int -> A.STUArray s Int Int -> A.STUArray s Int Int -> ST s ()
    loop i v0 v1 | i == m = pure ()
                 | otherwise = do
      A.unsafeWrite v1 0 (i + 1)
      let s1char = s1 `BS.unsafeIndex` i
      let go j prev | j == n = pure ()
                    | otherwise = do
            delCost <- v0 `A.unsafeRead` (j + 1)
            substCostBase <- v0 `A.unsafeRead` j
            let substCost = if s1char == s2 `BS.unsafeIndex` j then 0 else 1
            let res = min (substCost + substCostBase) $ 1 + min delCost prev
            A.unsafeWrite v1 (j + 1) res
            go (j + 1) res
      go 0 (i + 1)
      loop (i + 1) v1 v0

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

static long
lev_dist (const char *s1, unsigned long m
          const char *s2, unsigned long n)
{
    unsigned long m, n;
    unsigned long i, j;
    long *v0, *v1;
    long ret, *temp;

    /* Edge cases. */
    if (m == 0) {
        return n;
    } else if (n == 0) {
        return m;
    }

    v0 = malloc (sizeof (long) * (n + 1));
    v1 = malloc (sizeof (long) * (n + 1));

    if (v0 == NULL || v1 == NULL) {
        fprintf (stderr, "failed to allocate memory\n");
        exit (-1);
    }

    for (i = 0; i <= n; ++i) {
        v0[i] = i;
    }
    memcpy (v1, v0, sizeof(long) * (n + 1));

    for (i = 0; i < m; ++i) {
        v1[0] = i + 1;

        for (j = 0; j < n; ++j) {
            const long subst_cost = (s1[i] == s2[j]) ? v0[j] : (v0[j] + 1);
            const long del_cost = v0[j + 1] + 1;
            const long ins_cost = v1[j] + 1;

#if !defined(__GNUC__) || defined(__llvm__)
            if (subst_cost < del_cost) {
                v1[j + 1] = subst_cost;
            } else {
                v1[j + 1] = del_cost;
            }
#else
            v1[j + 1] = (subst_cost < del_cost) ? subst_cost : del_cost;
#endif
            if (ins_cost < v1[j + 1]) {
                v1[j + 1] = ins_cost;
            }
        }

        temp = v0;
        v0 = v1;
        v1 = temp;
    }

    ret = v0[n];
    free (v0);
    free (v1);
    return ret;
}

int
main ()
{
    const int len = 15000;
    int i;
    char s1[15001], s2[15001], s3[15001];
    clock_t start_time, exec_time;

    for (i = 0; i < len; ++i) {
        s1[i] = 'a';
        s2[i] = 'a';
        s3[i] = 'b';
    }
    s1[len] = s2[len] = s3[len] = '\0';

    start_time = clock ();

    printf ("%ld\n", lev_dist (s1, 15000, s2, 15000));
    printf ("%ld\n", lev_dist (s1, 15000, s3, 15000));

    exec_time = clock () - start_time;
    fprintf (stderr,
             "Finished in %.3fs\n",
             ((double) exec_time) / CLOCKS_PER_SEC);
    return 0;
}

def lev_dist(s1 : String, s2 : String) : Int
  m = s1.bytesize
  n = s2.bytesize

  # Edge cases.
  return n if m == 0
  return m if n == 0

  v0 = (Slice.new(n + 1) { |i| i }).to_unsafe
  v1 = (Slice.new(n + 1) { |i| i }).to_unsafe

  ca1, ca2 = s1.bytes, s2.bytes

  ca1.each_with_index do |c1, i|
    v1[0] = i + 1

    ca2.each_with_index do |c2, j|
      subst_cost = (c1 == c2) ? v0[j] : (v0[j] + 1)
      del_cost = v0[j + 1] + 1
      ins_cost = v1[j] + 1

      # [del_cost, ins_cost, subst_cost].min is slow.
      min_cost = (subst_cost < del_cost) ? subst_cost : del_cost
      if ins_cost < min_cost
        min_cost = ins_cost
      end
      v1[j + 1] = min_cost
    end

    v0, v1 = v1, v0
  end

  return v0[n]
end

s1 = "a" * 15_000
s2 = s1
s3 = "b" * 15_000

exec_time = -Time.monotonic.to_f

puts lev_dist(s1, s2)
puts lev_dist(s1, s3)

exec_time += Time.monotonic.to_f
STDERR.puts "Finished in #{"%.3f" % exec_time}s"

using System;
using System.Diagnostics;
using System.Linq;
using System.Text;

public class Program
{
    public static Int32 LevDist(string s1, string s2)
    {
        var ca1 = Encoding.UTF8.GetBytes(s1);
        var ca2 = Encoding.UTF8.GetBytes(s2);
        return LevDist(ca1, ca2);
    }

    public static Int32 LevDist(byte[] s1, byte[] s2)
    {
        var m = s1.Length;
        var n = s2.Length;

        // Edge cases.
        if (m == 0)
        {
            return n;
        }
        else if (n == 0)
        {
            return m;
        }

        Int32[] v0 = Enumerable.Range(0, n + 1).ToArray();
        var v1 = new Int32[n + 1];

        v0.CopyTo(v1, 0);

        for (var i = 0; i < m; ++i)
        {
            v1[0] = i + 1;

            for (var j = 0; j < n; ++j)
            {
                var substCost = (s1[i] == s2[j]) ? v0[j] : (v0[j] + 1);
                var delCost = v0[j + 1] + 1;
                var insCost = v1[j] + 1;

                v1[j + 1] = Math.Min(substCost, delCost);
                if (insCost < v1[j + 1])
                {
                    v1[j + 1] = insCost;
                }
            }

            var temp = v0;
            v0 = v1;
            v1 = temp;
        }

        return v0[n];
    }

    public static int Main()
    {
        string s1 = new String('a', 15000);
        string s2 = s1;
        string s3 = new String('b', 15000);

        Stopwatch execTimer = new Stopwatch();
        execTimer.Start();

        Console.WriteLine(LevDist(s1, s2));
        Console.WriteLine(LevDist(s1, s3));

        execTimer.Stop();
        double execTime = execTimer.ElapsedMilliseconds / 1000.0;

        Console.WriteLine($"Finished in {execTime:0.000}s");
        return 0;
    }
}

module main;
import core.time;
import std.stdio;
import std.algorithm : swap;
import std.array : array;
import std.range : iota, replicate;

long levDist(ref const string s1,
             ref const string s2) pure nothrow @trusted
{
    const auto m = s1.length;
    const auto n = s2.length;

    if (m == 0)
    {
        return n;
    }
    else if (n == 0)
    {
        return m;
    }

    long[] v0 = iota(0, long(n) + 1).array;
    long[] v1 = v0.dup;

    size_t i = 0;
    foreach (ref c1; s1)
    {
        v1[0] = i + 1;

        size_t j = 0;
        foreach (ref c2; s2)
        {
            const auto substCost = (c1 == c2) ? v0[j] : (v0[j] + 1);
            const auto delCost = v0[j + 1] + 1;
            const auto insCost = v1[j] + 1;

            // min(substCost, delCost, insCost) is slow.
            v1[j + 1] = (substCost < delCost) ? substCost : delCost;
            if (insCost < v1[j + 1])
            {
                v1[j + 1] = insCost;
            }

            ++j;
        }

        swap(v0, v1);
        ++i;
    }

    return v0[n];
}

void main(string[] args)
{
    string s1 = "a".replicate(15000);
    string s2 = s1;
    string s3 = "b".replicate(15000);

    auto startTime = MonoTime.currTime;

    writeln(levDist(s1, s2));
    writeln(levDist(s1, s3));

    auto endTime = MonoTime.currTime;
    auto execTime = (endTime - startTime).total!"msecs" / 1000.0;

    stderr.writefln("Finished in %.3fs", execTime);
}

package main

import (
    "bytes"
    "fmt"
    "os"
    "time"
)

func levDist(s1, s2 []byte) int {

    m := len(s1)
    n := len(s2)

    // Edge cases.
    if m == 0 {
        return n
    } else if n == 0 {
        return m
    }

    root := make([]int, (n+1)*2)

    v0 := root[:n+1]
    v1 := root[n+1:]
    for i, _ := range v0 {
        v0[i] = i
    }
    copy(v1, v0)

    for i, c1 := range s1 {
        v1[0] = i + 1

        for j, c2 := range s2 {
            substCost := v0[j]
            if c1 != c2 {
                substCost++
            }
            delCost := v0[j+1] + 1
            insCost := v1[j] + 1

            if substCost < delCost {
                v1[j+1] = substCost
            } else {
                v1[j+1] = delCost
            }
            if insCost < v1[j+1] {
                v1[j+1] = insCost
            }
        }

        v0, v1 = v1, v0
    }

    return v0[n]
}

func main() {

    s1 := bytes.Repeat([]byte("a"), 15000)
    s2 := s1
    s3 := bytes.Repeat([]byte("b"), 15000)

    startTime := time.Now()

    fmt.Println(levDist(s1, s2))
    fmt.Println(levDist(s1, s3))

        execTime := time.Now().Sub(startTime).Seconds()
    fmt.Fprintf(os.Stderr, "Finished in %.3fs\n", execTime)
}

use std::cmp::min;
use std::time::Instant;

fn lev_dist(s1: &str, s2: &str) -> i32 {
    let m = s1.len();
    let n = s2.len();

    // Edge cases.
    if m == 0 {
        return n as i32;
    } else if n == 0 {
        return m as i32;
    }

    let mut v0: Vec<i32> = (0..).take(n + 1).collect();
    let mut v1 = v0.to_vec();

    for (i, c1) in s1.bytes().enumerate() {
        unsafe {
            *v1.get_unchecked_mut(0) = i as i32 + 1;

            for (j, c2) in s2.bytes().enumerate() {
                let mut subst_cost = *v0.get_unchecked(j);
                if c1 != c2 {
                    subst_cost += 1;
                }
                let del_cost = *v0.get_unchecked(j + 1) + 1;
                let ins_cost = *v1.get_unchecked(j) + 1;

                let mut min_cost = min(subst_cost, del_cost);
                if ins_cost < min_cost {
                    min_cost = ins_cost;
                }
                *v1.get_unchecked_mut(j + 1) = min_cost;
            }
        }

        std::mem::swap(&mut v0, &mut v1);
    }

    return v0[n];
}

fn main() {
    let s1 = "a".repeat(15000);
    let s2 = &s1;
    let s3 = "b".repeat(15000);

    let start_time = Instant::now();

    println!("{}", lev_dist(&s1, &s2));
    println!("{}", lev_dist(&s1, &s3));

    let exec_time = start_time.elapsed().as_millis() as f64 / 1000.0;
    eprintln!("Finished in {:.3}s", exec_time);
}

const std = @import("std");
const time = std.time;
const Allocator = std.mem.Allocator;

pub fn lev_dist(allocator: *Allocator, s1: []const u8, s2: []const u8) !i32 {
    @setRuntimeSafety(false);
    const m = s1.len;
    const n = s2.len;

    // Edge cases.
    if (m == 0) {
        return @intCast(i32, n);
    } else if (n == 0) {
        return @intCast(i32, m);
    }

    var root = try allocator.alloc(i32, (n + 1) * 2);
    defer allocator.free(root);

    var v0 = root[0..(n + 1)];
    var v1 = root[(n + 1)..];

    for (v0) |*it, i| {
        it.* = @intCast(i32, i);
    }
    std.mem.copy(i32, v1, v0);

    for (s1) |c1, i| {
        v1[0] = @intCast(i32, i) + 1;

        for (s2) |c2, j| {
            const subst_cost = if (c1 == c2) v0[j] else (v0[j] + 1);
            const del_cost = v0[j + 1] + 1;
            const ins_cost = v1[j] + 1;

            // std.mem.min(i32, [_]i32{subst_cost, del_cost, ins_cost}) is slow.
            v1[j + 1] = if (subst_cost < del_cost) subst_cost else del_cost;
            if (ins_cost < v1[j + 1]) {
                v1[j + 1] = ins_cost;
            }
        }

        std.mem.swap([]i32, &v0, &v1);
    }

    return v0[n];
}

pub fn main() !void {
    const allocator = std.heap.page_allocator;
    const stdout = &(try std.io.getStdOut()).outStream().stream;

    const s1 = [_]u8{'a'} ** 15000;
    const s2 = s1;
    const s3 = [_]u8{'b'} ** 15000;

    var exec_timer = try time.Timer.start();

    try stdout.print("{}\n", try lev_dist(allocator, s1, s2));
    try stdout.print("{}\n", try lev_dist(allocator, s1, s3));

    const exec_time = @intToFloat(f64, exec_timer.read()) / time.ns_per_s;
    std.debug.warn("Finished in {d:.3}s\n", exec_time);
}

program main(output);
uses
  sysutils, dateutils;

function levDist(const s1: AnsiString; const s2: AnsiString): longint;
  var
    m, n: NativeUint;
    i, j: NativeUint;
    c1, c2: AnsiChar;
    v0, v1, temp: array of longint;
    substCost, delCost, insCost: longint;
  begin
    m := length(s1);
    n := length(s2);

    // Edge cases.
    if m = 0 then
      exit(n)
    else if n = 0 then
      exit(m);

    setLength(v0, n+1);
    for i := 0 to n do
      v0[i] := i;
    v1 := copy(v0, 0, n+1);

    i := 0;
    for c1 in s1 do
      begin
        j := 0;
        v1[0] := i + 1;

        for c2 in s2 do
          begin
            substCost := v0[j];
            if c1 <> c2 then
              inc(substCost);
            delCost := v0[j+1] + 1;
            insCost := v1[j] + 1;

            if substCost < delCost then
              v1[j+1] := substCost
            else
              v1[j+1] := delCost;
            if insCost < v1[j+1] then
              v1[j+1] := insCost;

            inc(j);
          end;

        temp := v0;
        v0 := v1;
        v1 := temp;

        inc(i);
      end;

    exit(v0[n]);
  end;

var
  i: integer;
  s1, s2, s3: AnsiString;
  startTime, execTime: TDateTime;
begin
  s1 := '';
  s3 := '';
  for i := 1 to 15000 do
    begin
      s1 := s1 + 'a';
      s3 := s3 + 'b';
    end;
  s2 := s1;

  startTime := now;

  writeln(levDist(s1, s2));
  writeln(levDist(s1, s3));

  execTime := secondSpan(startTime, now);
  writeln(stderr, format('Finished in %.3fs', [execTime]));
end.

import strformat, strutils, times

{.push checks: off.}
func levDist(s1, s2: string): int32 =
  let m = s1.len
  let n = s2.len

  # Edge cases.
  if m == 0: return int32(n)
  elif n == 0: return int32(m)

  var v0 = newSeq[int32](n + 1)
  for i, _ in v0:
    v0[i] = int32(i)

  var v1 = v0

  for i, c1 in s1:
    v1[0] = int32(i) + 1

    for j, c2 in s2:
      let delCost = v0[j + 1] + 1
      let insCost = v1[j] + 1
      var substCost = v0[j]
      if c1 != c2:
        inc(substCost)

      # min([substCost, delCost, insCost]) is slow.
      v1[j + 1] = min(substCost, delCost)
      if insCost < v1[j + 1]:
        v1[j + 1] = insCost

    swap(v0, v1)

  result = v0[n]
{.pop.}

let s1 = repeat("a", 15000)
let s2 = s1
let s3 = repeat("b", 15000)

let startTime = cpuTime()

echo levDist(s1, s2)
echo levDist(s1, s3)

let execTime = cpuTime() - startTime;
stderr.write &"Finished in {execTime:.3f}s\n";

import java.util.Arrays;
import java.util.stream.LongStream;
import java.lang.Math;

public class LevDist
{
    public static long levDist(String s1, String s2)
    {
        return levDist(s1.getBytes(), s2.getBytes());
    }

    public static long levDist(byte[] s1, byte[] s2)
    {
        int m = s1.length;
        int n = s2.length;

        // Edge cases.
        if (m == 0) {
            return n;
        } else if (n == 0) {
            return m;
        }

        long[] v0 = LongStream.range(0, n + 1).toArray();
        long[] v1 = v0.clone();

        int i = 0, j;
        for (byte c1 : s1) {
            v1[0] = i + 1;

            j = 0;
            for (byte c2 : s2) {
                long substCost = (c1 == c2) ? v0[j] : (v0[j] + 1);
                long delCost = v0[j + 1] + 1;
                long insCost = v1[j] + 1;

                v1[j + 1] = Math.min(substCost, delCost);
                if (insCost < v1[j + 1]) {
                    v1[j + 1] = insCost;
                }

                ++j;
            }

            long[] temp = v0;
            v0 = v1;
            v1 = temp;

            ++i;
        }

        return v0[n];
    }

    public static void main(String[] args)
    {
        byte[] s1 = new byte[15000];
        byte[] s2 = s1;
        byte[] s3 = new byte[15000];

        Arrays.fill(s1, (byte) 'a');
        Arrays.fill(s3, (byte) 'b');

        long execTime = -System.nanoTime();

        System.out.println(levDist(s1, s2));
        System.out.println(levDist(s1, s3));

        execTime += System.nanoTime();

        System.err.printf("Finished in %.3fs%n", execTime / 1000000000.0);
    }
}

#!/usr/bin/env julia
using Base: @pure, stderr
using Printf

@pure function lev_dist(s1::AbstractString, s2::AbstractString)::Int32
    m, n = sizeof(s1), sizeof(s2)

    m == 0 && return n
    n == 0 && return m

    ca1, ca2 = codeunits(s1), codeunits(s2)

    v0::Vector{Int32} = collect(0:n)
    v1 = copy(v0)

    @inbounds begin
        for (i, c1) in enumerate(ca1)
            v1[1] = i

            for (j, c2) in enumerate(ca2)
                subst_cost = v0[j] + ((c1 === c2) ? 0 : 1)
                del_cost = v0[j + 1] + 1
                ins_cost = v1[j] + 1

                v1[j + 1] = min(subst_cost, del_cost, ins_cost)
            end
            v0, v1 = v1, v0
        end
    end

    return v0[n + 1]
end

let
    s1 = 'a'^15000
    s2 = s1
    s3 = 'b'^15000

    exec_time = @elapsed begin
        println(lev_dist(s1, s2))
        println(lev_dist(s1, s3))
    end
    @printf(stderr, "Finished in %.3fs\n", exec_time)
end

function stringToByteArray(s) {
  let a = [];
  for (let c of s) {
    c = c.charCodeAt(0);
    do {
      a.unshift(c & 0xFF);
      c >>= 8;
    } while (c !== 0);
  }
  return a;
}

function levDist(s1, s2) {
  if (typeof s1 === "string" || s1 instanceof String) {
    s1 = stringToByteArray(s1);
  }
  if (typeof s2 === "string" || s2 instanceof String) {
    s2 = stringToByteArray(s2);
  }

  const m = s1.length;
  const n = s2.length;

  // Edge cases.
  if (m == 0) {
    return n;
  } else if (n == 0) {
    return m;
  }

  let v0 = [];
  for (let i = 0; i <= n; ++i) {
    v0[i] = i;
  }
  let v1 = v0.slice();

  for (let i = 0; i < m; ++i) {
    v1[0] = i + 1;

    for (let j = 0; j < n; ++j) {
      const substCost = v0[j] + ((s1[i] === s2[j]) ? 0 : 1);
      const delCost = v0[j + 1] + 1;
      const insCost = v1[j] + 1;

      // Math.min(substCost, delCost, insCost) is slow.
      v1[j + 1] = (substCost < delCost) ? substCost : delCost;
      if (insCost < v1[j + 1]) {
        v1[j + 1] = insCost;
      }
    }

    [v0, v1] = [v1, v0];
  }

  return v0[n];
}

var s1 = new Uint8Array(15000);
var s2 = s1;
var s3 = new Uint8Array(s1.length);

for (let i = 0; i < s1.length; ++i) {
    s1[i] = "a".charCodeAt(0);
    s3[i] = "b".charCodeAt(0);
}

var execTime = -Date.now();

console.log(levDist(s1, s2));
console.log(levDist(s1, s3));

execTime += Date.now();
console.log(`Finished in ${(execTime / 1000).toFixed(3)}s`);

#!/usr/bin/env python3
import sys
import time
from typing import AnyStr

def lev_dist(s1: AnyStr, s2: AnyStr) -> int:
    if isinstance(s1, str): s1 = s1.encode()
    if isinstance(s2, str): s2 = s2.encode()

    m = len(s1)
    n = len(s2)

    # Edge cases.
    if m == 0: return n
    elif n == 0: return m

    v0 = list(range(0, n + 1))
    v1 = v0[:]

    for i, c1 in enumerate(s1):
        v1[0] = i + 1

        for j, c2 in enumerate(s2):
            subst_cost = v0[j] if c1 == c2 else (v0[j] + 1)
            del_cost = v0[j + 1] + 1
            ins_cost = v1[j] + 1

            # min(subst_cost, del_cost, ins_cost) is slow.
            min_cost = subst_cost if subst_cost < del_cost else del_cost
            if ins_cost < min_cost:
                min_cost = ins_cost
            v1[j + 1] = min_cost

        v0, v1 = v1, v0

    return v0[n]

if __name__ == "__main__":
    s1 = b"a" * 15_000
    s2 = s1
    s3 = b"b" * 15_000

    exec_time = -time.monotonic()

    print(lev_dist(s1, s2))
    print(lev_dist(s1, s3))

    exec_time += time.monotonic()
    print(f"Finished in {exec_time:.3f}s", file=sys.stderr)

#!/usr/bin/env lua

function levDist (s1, s2)
  local m = s1:len()
  local n = s2:len()

  -- Edge cases
  if m == 0 then return n end
  if n == 0 then return m end

  local ct1, ct2 = {}, {}
  for i = 1, #s1 do
      ct1[i] = s1:sub(i, i)
  end
  for i = 1, #s2 do
      ct2[i] = s2:sub(i, i)
  end

  local v0, v1 = {}, {}
  for i = 1, n + 1 do
    v0[i] = i - 1
    v1[i] = i - 1
  end

  local minCost, substCost, delCost, insCost
  for i, c1 in pairs(ct1) do
    v1[1] = i

    for j, c2 in pairs(ct2) do
      substCost = (c1 == c2) and v0[j] or (v0[j] + 1)
      delCost = v0[j + 1] + 1
      insCost = v1[j] + 1

      -- math.min(substCost, delCost, insCost) is slow.
      minCost = (substCost < delCost) and substCost or delCost
      if insCost < minCost then
        minCost = insCost
      end
      v1[j + 1] = minCost
    end

    v0, v1 = v1, v0
  end

  return v0[n + 1]
end

s1 = string.rep("a", 15000)
s2 = s1
s3 = string.rep("b", 15000)

execTime = -os.clock()

print(levDist(s1, s2))
print(levDist(s1, s3))

execTime = execTime + os.clock()
io.stderr:write(string.format("Finished in %.3fs\n", execTime))

#!/usr/bin/env php
<?php

function lev_dist(string $s1, string $s2): int
{
    $m = strlen($s1);
    $n = strlen($s2);

    // Edge cases.
    if ($m == 0) {
        return $n;
    } elseif ($n == 0) {
        return $m;
    }

    $ca1 = $ca2 = [];
    for ($i = 0; $i < $m; ++$i) {
        $ca1[] = ord($s1[$i]);
    }
    for ($i = 0; $i < $n; ++$i) {
        $ca2[] = ord($s2[$i]);
    }

    $v0 = range(0, $n + 1);
    $v1 = $v0;

    foreach ($ca1 as $i => $c1) {
        $v1[0] = $i + 1;

        foreach ($ca2 as $j => $c2) {
            $subst_cost = ($c1 == $c2) ? $v0[$j] : ($v0[$j] + 1);
            $del_cost = $v0[$j + 1] + 1;
            $ins_cost = $v1[$j] + 1;

            // min($subst_cost, $del_cost, $ins_cost) is slow.
            $min_cost = ($subst_cost < $del_cost) ? $subst_cost : $del_cost;
            if ($ins_cost < $min_cost) {
                $min_cost = $ins_cost;
            }
            $v1[$j + 1] = $min_cost;
        }

        [$v0, $v1] = [$v1, $v0];
    }

    return $v0[$n];
}

$s1 = str_repeat('a', 15000);
$s2 = $s1;
$s3 = str_repeat('b', 15000);

$exec_time = -hrtime(true);

echo lev_dist($s1, $s2), "\n";
echo lev_dist($s1, $s3), "\n";

$exec_time += hrtime(true);
fprintf(STDERR, "Finished in %.3fs\n", $exec_time / 1000000000);

#!/usr/bin/env hhvm

function lev_dist(string $s1, string $s2): int {
  $m = \strlen($s1);
  $n = \strlen($s2);

  // Edge cases.
  if ($m == 0) {
    return $n;
  } else if ($n == 0) {
    return $m;
  }

  $ca1 = $ca2 = vec[];
  for ($i = 0; $i < $m; ++$i) {
    $ca1[] = \ord($s1[$i]);
  }
  for ($i = 0; $i < $n; ++$i) {
    $ca2[] = \ord($s2[$i]);
  }

  $v0 = vec(\range(0, $n + 1));
  $v1 = $v0;

  foreach ($ca1 as $i => $c1) {
    $v1[0] = $i + 1;

    foreach ($ca2 as $j => $c2) {
      $subst_cost = ($c1 == $c2) ? $v0[$j] : ($v0[$j] + 1);
      $del_cost = $v0[$j + 1] + 1;
      $ins_cost = $v1[$j] + 1;

      // \min($subst_cost, $del_cost, $ins_cost) is slow.
      $min_cost = ($subst_cost < $del_cost) ? $subst_cost : $del_cost;
      if ($ins_cost < $min_cost) {
        $min_cost = $ins_cost;
      }
      $v1[$j + 1] = $min_cost;
    }

    list($v0, $v1) = vec[$v1, $v0];
  }

  return $v0[$n];
}

<<__EntryPoint>>
function main(): void {
  $s1 = \str_repeat('a', 15000);
  $s2 = $s1;
  $s3 = \str_repeat('b', 15000);

  $exec_time = -\clock_gettime_ns(\CLOCK_MONOTONIC);

  echo lev_dist($s1, $s2), "\n";
  echo lev_dist($s1, $s3), "\n";

  $exec_time += \clock_gettime_ns(\CLOCK_MONOTONIC);
  \fprintf(\STDERR, "Finished in %.3fs\n", $exec_time / 1000000000);
}

#!/usr/bin/env nqp
use nqp;

sub str-to-byte-array(str $s) {
    my @a;
    for nqp::split('', $s) -> $c {
        $c := nqp::ord($c);
        repeat {
            my uint8 $b := $c +& 0xFF;
            @a.unshift($b);
            $c := nqp::bitshiftr_i($c, 8);
        } while $c != 0;
    }
    return @a;
}

sub lev-dist(str $s1, str $s2) {
    my @ca1 := str-to-byte-array($s1);
    my @ca2 := str-to-byte-array($s2);

    my $m := nqp::elems(@ca1);
    my $n := nqp::elems(@ca2);

    # Edge cases.
    return $n if $m == 0;
    return $m if $n == 0;

    my @v0[$n + 1];
    my @v1[$n + 1];

    my int $i := 0;
    while $i <= $n {
        @v0[$i] := $i;
        @v1[$i] := $i;
        ++$i;
    }

    $i := 0;
    for @ca1 -> $c1 {
        @v1[0] := $i + 1;

        my int $j := 0;
        for @ca2 -> $c2 {
            my int $subst-cost := @v0[$j] + (($c1 == $c2) ?? 0 !! 1);
            my int $del-cost := @v0[$j + 1] + 1;
            my int $ins-cost := @v1[$j] + 1;

            my int $min-cost := ($subst-cost < $del-cost) ?? $subst-cost !! $del-cost;
            if $ins-cost < $min-cost {
                $min-cost := $ins-cost;
            }
            @v1[$j + 1] := $min-cost;

            ++$j;
        }

        my @temp := @v0;
        @v0 := @v1;
        @v1 := @temp;

        ++$i;
    }

    return @v0[$n];
}

sub MAIN(*@ARGS) {
    my str $s1 := nqp::x('a', 15_000);
    my str $s2 := $s1;
    my str $s3 := nqp::x('b', 15_000);

    my num $start-time := nqp::time_n();

    say(lev-dist($s1, $s2));
    say(lev-dist($s1, $s3));

    my num $exec-time := nqp::sub_n(nqp::time_n(), $start-time);
    stderr().print(nqp::sprintf("Finished in %.3fs\n", [$exec-time]));
}

#!/usr/bin/env ruby
# encoding: utf-8

def lev_dist(s1, s2)
  m = s1.bytesize
  n = s2.bytesize

  # Edge cases.
  return n if m == 0
  return m if n == 0

  v0 = (0..n).to_a
  v1 = v0.dup

  ca1, ca2 = s1.bytes, s2.bytes

  ca1.each_with_index do |c1, i|
    v1[0] = i + 1

    ca2.each_with_index do |c2, j|
      subst_cost = (c1 == c2) ? v0[j] : (v0[j] + 1)
      del_cost = v0[j + 1] + 1
      ins_cost = v1[j] + 1

      # [del_cost, ins_cost, subst_cost].min is slow.
      min_cost = (subst_cost < del_cost) ? subst_cost : del_cost
      if ins_cost < min_cost
        min_cost = ins_cost
      end
      v1[j + 1] = min_cost
    end

    v0, v1 = v1, v0
  end

  return v0[n]
end

s1 = "a" * 15_000
s2 = s1
s3 = "b" * 15_000

exec_time = -Process.clock_gettime(Process::CLOCK_MONOTONIC)

puts lev_dist(s1, s2)
puts lev_dist(s1, s3)

exec_time += Process.clock_gettime(Process::CLOCK_MONOTONIC)
STDERR.puts "Finished in #{"%.3f" % exec_time}s"

#!/usr/bin/env raku
=encoding utf8;
use v6;

multi lev-dist(Str:D $s1, Str:D $s2 --> Int:D) {
    my $ca1 := buf8.new($s1.encode);
    my $ca2 := buf8.new($s2.encode);

    return lev-dist($ca1, $ca2);
}

multi lev-dist(buf8:D $s1, buf8:D $s2 --> Int:D) {
    my $m := $s1.bytes;
    my $n := $s2.bytes;

    # Edge cases.
    return $n if $m == 0;
    return $m if $n == 0;

    my @ca1 = $s1.list;
    my @ca2 = $s2.list;

    my @v0[$n + 1] = 0..$n;
    my @v1[$n + 1] = 0..$n;

    for @ca1.kv -> $i, $c1 {
        @v1[0] = $i + 1;

        for @ca2.kv -> $j, $c2 {
            my $subst-cost := @v0[$j] + (($c1 == $c2) ?? 0 !! 1);
            my $del-cost := @v0[$j + 1] + 1;
            my $ins-cost := @v1[$j] + 1;

            # min($subst-cost, $del-cost, $ins-cost) is slow.
            my $min-cost := ($subst-cost < $del-cost) ?? $subst-cost !! $del-cost;
            if $ins-cost < $min-cost {
                $min-cost = $ins-cost;
            }
            @v1[$j + 1] = $min-cost;
        }

        my @temp := @v0;
        @v0 := @v1;
        @v1 := @temp;
    }

    return @v0[$n];
}

sub MAIN() {
    my $s1 := 'a' x 15_000;
    my $s2 := $s1;
    my $s3 := 'b' x 15_000;

    my $start-time := now;

    say(lev-dist($s1, $s2));
    say(lev-dist($s1, $s3));

    my $exec-time := now - $start-time;
    note(sprintf("Finished in %.3fs", $exec-time));
}

#!/usr/bin/env octave
1;

function retval = lev_dist (s1, s2)
  if (!isvector (s1) || iscell (s1) || !isvector (s2) || iscell (s2))
    error ("lev_dist: Incompatible types in assignment");
  endif

  m = length (s1);
  n = length (s2);

  if (m == 0)
    retval = n;
  elseif (n == 0)
    retval = m;
  else
    v0 = [0:n];
    v1 = v0;

    for i = 1:m
      v1(1) = i;

      for j = 1:n
        subst_cost = v0(j) + (s1(i) != s2(j));
        del_cost = v0(j + 1) + 1;
        ins_cost = v1(j) + 1;

        # min ([subst_cost, del_cost, ins_cost]) is slow.
        if (subst_cost < del_cost)
          min_cost = subst_cost;
        else
          min_cost = del_cost;
        endif
        if (ins_cost < min_cost)
          min_cost = ins_cost;
        endif
        v1(j + 1) = min_cost;
      endfor

      [v0, v1] = deal (v1, v0);
    endfor

    retval = v0(n + 1);
  endif
endfunction

function main ()
  s1 = repmat (["a"], 15_000, 1);
  s2 = s1;
  s3 = repmat (["b"], 15_000, 1);
  tic ();
  printf ("%d\n", lev_dist (s1, s2));
  printf ("%d\n", lev_dist (s1, s3));
  exec_time = toc ();
  fprintf (stderr, "Finished in %.3fs\n", exec_time);
endfunction

main ();