[C++] Levenshtein Distance Algorithm

---

---

Levenshtein Distance Algorithm: C++ Implementation

by Anders Sewerin Johansen

// Include STL string type

#include 

// Include STL vector type (dynamic array)

#include 

int distance(const std::string source, const std::string target) {

  // Step 1

  const int n = source.length();
  const int m = target.length();
  if (n == 0) {
    return m;
  }
  if (m == 0) {
    return n;
  }

  // Good form to declare a TYPEDEF

  typedef std::vector< std::vector > Tmatrix; 

  Tmatrix matrix(n+1);

  // Size the vectors in the 2.nd dimension. Unfortunately C++ doesn't
  // allow for allocation on declaration of 2.nd dimension of vec of vec

  for (int i = 0; i <= n; i++) {
    matrix[i].resize(m+1);
  }

  // Step 2

  for (int i = 0; i <= n; i++) {
    matrix[i][0]=i;
  }

  for (int j = 0; j <= m; j++) {
    matrix[0][j]=j;
  }

  // Step 3

  for (int i = 1; i <= n; i++) {

    const char s_i = source[i-1];

    // Step 4

    for (int j = 1; j <= m; j++) {

      const char t_j = target[j-1];

      // Step 5

      int cost;
      if (s_i == t_j) {
        cost = 0;
      }
      else {
        cost = 1;
      }

      // Step 6

      const int above = matrix[i-1][j];
      const int left = matrix[i][j-1];
      const int diag = matrix[i-1][j-1];
      const int cell = min( above + 1, min(left + 1, diag + cost));

      // Step 6A: Cover transposition, in addition to deletion,
      // insertion and substitution. This step is taken from:
      // Berghel, Hal ; Roach, David : "An Extension of Ukkonen's 
      // Enhanced Dynamic Programming ASM Algorithm"
      // (http://www.acm.org/~hlb/publications/asm/asm.html)

      if (i>2 && j>2) {
        int trans=matrix[i-2][j-2]+1;
        if (source[i-2]!=t_j) trans++;
        if (s_i!=target[j-2]) trans++;
        if (cell>trans) cell=trans;
      }

      matrix[i][j]=cell;
    }
  }

  // Step 7

  return matrix[n][m];
}