# include <cstring>
# include <iomanip>
# include <iostream>

using namespace std;

# include "levenshtein_distance.hpp"

//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    i4_min() returns the minimum of two I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int I1, I2, two integers to be compared.
//
//  Output:
//
//    int I4_MIN, the smaller of I1 and I2.
//
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int levenshtein_distance ( int m, string s, int n, string t )

//****************************************************************************80
//
//  Purpose:
//
//    levenshtein_distance() computes the Levenshtein distance between strings.
//
//  Discussion:
//
//    Let S and T be source and target strings.  Consider the task of
//    converting S to T in the minimal number of steps, involving
//    * Insertion: insert a new character
//    * Deletion: delete a character
//    * Substitution: swap one character for another.
//    The Levenshtein distance from S to T is the minimal number of such
//    steps required to transform S into T.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    19 March 2018
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, the length of string S.
//
//    string S, the first string.
//
//    int N, the length of string T.
//
//    string T, the second string.
//
//  Output:
//
//    int LEVENSHTEIN_DISTANCE, the Levenshtein distance between the
//    two strings.
//
{
  int *d;
  int distance;
  int i;
  int j;
  int substitution_cost;

  d = new int[(m+1)*(n+1)];

  d[0+0*(m+1)] = 0;
//
//  Source prefixes can be transformed into empty string by
//  dropping all characters,
//
  for ( i = 1; i <= m; i++ )
  {
    d[i+0*(m+1)] = i;
  }
//
//  Target prefixes can be reached from empty source prefix
//  by inserting every character.
//
  for ( j = 1; j <= n; j++ )
  {
    d[0+j*(m+1)] = j;
  }

  for ( j = 1; j <= n; j++ )
  {
    for ( i = 1; i <= m; i++ )
    {
      if ( s[i-1] == t[j-1] )
      {
        substitution_cost = 0;
      }
      else
      {
        substitution_cost = 1;
      }
      d[i+j*(m+1)] = i4_min ( d[i-1+j*(m+1)] + 1, 
                     i4_min ( d[i+(j-1)*(m+1)] + 1, 
                              d[i-1+(j-1)*(m+1)] + substitution_cost ) );
    }
  }
 
  distance = d[m+n*(m+1)];

  delete [] d;

  return distance;
}