最短编辑距离算法

最短编辑距离算法，在搜索引擎开发中应用很多，比如相关词等
还可用于比较2个页面是否相同，如果不同需要多少步才能相同。把相同的去掉，提取不同的，这样可以达到自动提取正文的目的，使得文本提取不局限于具体的网页结构，打破模板的缺陷，是垂直搜索更具通用性。

package com.lietu.relatedwords;
public class Distance {
// ****************************
// Get minimum of three values
// ****************************
private static int Minimum(int a, int b, int c) {
  int mi;
  mi = a;
  if (b < mi) {
   mi = b;
  }
  if (c < mi) {
   mi = c;
  }
  return mi;
}
/**
  *
  * @param s 输入源串
  * @param t 输入目标串
  * @return 源串和目标串之间的编辑距离
  */
public static int LD(String s, String t) {
  int d[][]; // matrix
  int n; // length of s
  int m; // length of t
  int i; // iterates through s
  int j; // iterates through t
  char s_i; // ith character of s
  char t_j; // jth character of t
  int cost; // cost
  // Step 1 初始化
  n = s.length();
  m = t.length();
  if (n == 0) {
   return m;
  }
  if (m == 0) {
   return n;
  }
  d = new int[n + 1][m + 1];
  // Step 2 Initialize the first row to 0..n.
  for (i = 0; i <= n; i++) {
   d[0] = i;
  }
  //Initialize the first column to 0..m.
  for (j = 0; j <= m; j++) {
   d[0][j] = j;
  }
  // Step 3 Examine each character of s (i from 1 to n).
  for (i = 1; i <= n; i++) {
   s_i = s.charAt(i - 1);
   // Step 4 Examine each character of t (j from 1 to m).
   for (j = 1; j <= m; j++) {
    t_j = t.charAt(j - 1);
    // Step 5
    // If s equals t[j], the cost is 0.
    //  If s doesn't equal t[j], the cost is 1.
    if (s_i == t_j) {
     cost = 0;
    } else {
     cost = 1;
    }
    // Step 6
    //Set cell d of the matrix equal to the minimum of:
    //a. The cell immediately above plus 1: d + 1.
    //b. The cell immediately to the left plus 1: d + 1.
    //c. The cell diagonally above and to the left plus the cost: d + cost.
    d[j] = Minimum(d[j] + 1, d[j - 1] + 1,
      d[j - 1] + cost);
   }
  }
  // Step 7
  // After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].
  return d[n][m];
}
}